Linear Regression#

Linear regression is one of the most popular regression algorithms and produces good predictions for well-prepared data. Its optimization function computes coefficients to express a response column as a linear relationship of its predictors.

You must verify the Gauss-Markov assumptions when using linear regression algorithms:

Linearity : the parameters we are estimating using the OLS method must be linear.
Non-Collinearity : the regressors being calculated aren’t perfectly correlated with each other.
Exogeneity : the regressors aren’t correlated with the error term.
Homoscedasticity : no matter what the values of our regressors might be, the error of the variance is constant.

To create a good linear regression model, it’s important to:

Impute missing values
Encode categorical features (linear regression only accepts numerical variables)
Compute the correlation matrix to retrieve highly-correlated predictors
Decompose the data (optional)
Normalize the data (optional, but recommended)

Example without decomposition#

Let’s use the ‘africa_education’ dataset to compute a linear regression model of students’ performance in school.

[1]:

import verticapy as vp
vp.set_option("plotting_lib","highcharts")
africa = vp.read_csv("data/africa_education.csv")
africa = africa.select(["(zralocp + zmalocp) / 2 AS student_score",
                        "zraloct AS teacher_score",
                        "XNUMYRS AS teacher_year_teaching",
                        "numstu AS number_students_school",
                        "PENGLISH AS english_at_home",
                        "PTRAVEL AS travel_distance",
                        "PTRAVEL2 AS means_of_travel",
                        "PMOTHER AS m_education",
                        "PFATHER AS f_education",
                        "PLIGHT AS source_of_lighting",
                        "PABSENT AS days_absent",
                        "PREPEAT AS repeated_grades",
                        "zpsit AS sitting_place",
                        "PAGE AS age",
                        "zpses AS socio_eco_statut",
                        "country_long AS country"])
display(africa)

	123 student_score Float(22)	123 teacher_score Float(22)	123 teacher_year_teaching Numeric(9)	123 number_students_school Integer	Abc english_at_home Varchar(32)	Abc travel_distance Varchar(22)	Abc means_of_travel Varchar(26)	Abc Varchar(68)	Abc Varchar(68)	Abc source_of_lighting Varchar(24)	123 days_absent Integer	Abc repeated_grades Varchar(20)	Abc sitting_place Varchar(54)	123 age Integer	123 socio_eco_statut Numeric(9)	Abc country Varchar(24)
1	681.138508424325	[null]	26.0	24	ALL THE TIME	>0.5-1KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	15.0	South Africa
2	425.993367323877	581.994282503848	10.0	23	SOMETIMES	>4.5-5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Namibia
3	534.329515370892	581.994282503848	10.0	23	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	7.0	Namibia
4	536.690743411639	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia
5	569.392927563969	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	9.0	Namibia
6	542.037992351316	581.994282503848	10.0	23	MOST OF THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	11.0	Namibia
7	573.771789981159	581.994282503848	10.0	23	MOST OF THE TIME	>1.5-2KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	11.0	Namibia
8	589.279157441376	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	12.0	Namibia
9	496.740841813343	581.994282503848	10.0	23	SOMETIMES	>2.5-3KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	14	12.0	Namibia
10	535.805274812767	601.83282358059	1.0	22	ALL THE TIME	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Mozambique
11	420.509155247374	715.046036359878	1.0	25	ALL THE TIME	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	3.0	Zanzibar
12	504.298378016207	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	3.0	Zanzibar
13	450.768711398358	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	4.0	Zanzibar
14	441.927245450751	715.046036359878	1.0	25	ALL THE TIME	>1-1.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Zanzibar
15	469.987298066451	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Zanzibar
16	445.259642792635	715.046036359878	1.0	25	ALL THE TIME	>4KM-4.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	6.0	Zanzibar
17	551.071920864503	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	6.0	Zanzibar
18	473.825234391116	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	7.0	Zanzibar
19	544.095820873929	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Zanzibar
20	564.874824604798	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	8.0	Zanzibar
21	386.940445160128	601.83282358059	11.0	23	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	3.0	Mozambique
22	458.501728934408	648.090960225876	3.0	23	SOMETIMES	>2-2.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	5.0	Mozambique
23	460.360232184133	601.83282358059	11.0	23	ALL THE TIME	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	15	7.0	Mozambique
24	457.035551231015	648.090960225876	3.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Mozambique
25	504.282977573042	648.090960225876	3.0	23	ALL THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Mozambique
26	475.872247772718	601.83282358059	11.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	16	10.0	Mozambique
27	503.899980617811	613.278135740248	3.0	7	ALL THE TIME	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	15	2.0	Mozambique
28	480.484906064866	613.278135740248	3.0	7	ALL THE TIME	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	15	3.0	Mozambique
29	516.744491629541	715.332169163869	20.0	25	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
30	394.65259093503	715.332169163869	20.0	25	NEVER	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia
31	506.128325450387	715.332169163869	20.0	25	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	7.0	Namibia
32	440.401203829463	715.332169163869	20.0	25	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	8.0	Namibia
33	453.010211603314	715.332169163869	20.0	25	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	11	8.0	Namibia
34	498.219068060275	715.332169163869	20.0	25	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	11.0	Namibia
35	359.385615553614	648.090960225876	30.0	16	ALL THE TIME	UP TO 0.5KM	WALK			GAS	0	NEVER	I have my own sitting place	14	[null]	Mozambique
36	525.275821925396	648.090960225876	30.0	16	ALL THE TIME	UP TO 0.5KM	WALK			GAS	0	NEVER	I have my own sitting place	17	[null]	Mozambique
37	457.035551231015	648.090960225876	30.0	16	ALL THE TIME	UP TO 0.5KM	WALK			GAS	0	NEVER	I have my own sitting place	12	[null]	Mozambique
38	509.337990443557	648.090960225876	30.0	16	ALL THE TIME	UP TO 0.5KM	WALK			GAS	0	NEVER	I have my own sitting place	12	[null]	Mozambique
39	434.970625831997	648.090960225876	30.0	16	SOMETIMES	UP TO 0.5KM	WALK			GAS	0	NEVER	I have my own sitting place	17	[null]	Mozambique
40	[null]	709.132625077388	2.0	16	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	17	4.0	Mozambique
41	428.988211440412	727.826634938163	8.0	23	SOMETIMES	>5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	2.0	Namibia
42	532.255684949772	727.826634938163	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	2.0	Namibia
43	392.664714363554	767.599094692976	8.0	20	ALL THE TIME	>3-3.5KM	WALK			CANDLE	0	NEVER	No place/share	13	4.0	Zambia
44	415.95588691273	727.826634938163	8.0	23	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	4.0	Namibia
45	479.525184773189	727.826634938163	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
46	410.328608434232	727.826634938163	8.0	23	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
47	425.993367323877	727.826634938163	8.0	23	SOMETIMES	>3-3.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	4.0	Namibia
48	409.430742983857	727.826634938163	8.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	5.0	Namibia
49	460.605886281468	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
50	560.188989035577	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
51	378.486087509513	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	14	6.0	Namibia
52	516.831361986859	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	6.0	Namibia
53	557.155342162198	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
54	631.282997954796	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
55	501.677328837489	727.826634938163	8.0	23	SOMETIMES	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	18	6.0	Namibia
56	466.248533790025	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
57	594.667991916549	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
58	619.020904331767	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
59	422.517903579997	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
60	514.338009258817	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	6.0	Namibia
61	512.766872215611	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
62	456.266205420931	767.599094692976	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Zambia
63	380.388263378723	727.826634938163	8.0	23	SOMETIMES	>5KM	CAR			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	8.0	Namibia
64	421.344721387902	767.599094692976	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	11	8.0	Zambia
65	486.501284763764	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	9.0	Namibia
66	453.357504553945	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	9.0	Namibia
67	498.219068060275	691.392391229917	6.0	24	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	9.0	Namibia
68	514.807687171462	691.392391229917	6.0	24	NEVER	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	10.0	Namibia
69	565.065579807459	781.810357291219	12.0	21	MOST OF THE TIME	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	13.0	South Africa
70	626.714865963592	691.392391229917	8.0	21	ALL THE TIME	UP TO 0.5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	11	14.0	South Africa
71	457.134154158281	781.810357291219	12.0	21	SOMETIMES	>5KM	BUS/TRUCK/VAN			ELECTRIC	0	NEVER	I have my own sitting place	13	14.0	South Africa
72	510.499756960558	668.40638930927	9.0	20	MOST OF THE TIME	>1-1.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	16	2.0	Uganda
73	494.235377715545	668.40638930927	9.0	20	SOMETIMES	>1.5-2KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	17	2.0	Uganda
74	365.266644239282	635.405739248921	1.0	13	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	2.0	Zambia
75	541.173490674172	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	3.0	Namibia
76	455.36049792936	691.392391229917	8.0	20	SOMETIMES	>5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	15	3.0	Malawi
77	422.517903579997	691.392391229917	8.0	20	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	12	5.0	Malawi
78	398.31103066659	703.219213794897	1.0	21	MOST OF THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Malawi
79	395.120560563494	679.756323867598	1.0	22	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia
80	503.716941803917	691.392391229917	6.0	49	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
81	427.462485792718	646.278785800597	8.0	18	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	13	6.0	Zambia
82	600.91272658553	691.392391229917	6.0	49	SOMETIMES	>2-2.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
83	565.065579807459	691.392391229917	6.0	49	SOMETIMES	>5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
84	540.204883338675	691.392391229917	6.0	49	MOST OF THE TIME	>2.5-3KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Namibia
85	558.474690429794	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	7.0	Namibia
86	575.637662232951	691.392391229917	6.0	49	NEVER	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Namibia
87	439.680053114802	691.392391229917	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Malawi
88	353.773643278958	635.405739248921	1.0	13	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Zambia
89	488.376137298698	691.392391229917	6.0	49	SOMETIMES	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Namibia
90	480.908033418792	691.392391229917	6.0	49	MOST OF THE TIME	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia
91	535.286927844308	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia
92	408.529715955022	703.219213794897	1.0	21	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	15	9.0	Malawi
93	385.53865385057	646.278785800597	8.0	18	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	9.0	Zambia
94	528.310827853733	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	10.0	Namibia
95	548.67653911654	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	10.0	Namibia
96	588.423257247566	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Namibia
97	583.034422772394	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Namibia
98	455.36049792936	691.392391229917	8.0	20	NEVER	>3.5-4KM	WALK			ELECTRIC	0	NEVER	No place/share	14	10.0	Malawi
99	459.986311593889	691.392391229917	6.0	49	SOMETIMES	>2.5-3KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	11.0	Namibia
100	594.667991916549	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	12.0	Namibia

Rows: 1-100 | Columns: 16

First, let’s look for missing values.

[2]:

africa.count_percent()

[2]:

	count	percent
"number_students_school"	59909.0	100.0
"english_at_home"	59909.0	100.0
"travel_distance"	59909.0	100.0
"means_of_travel"	59909.0	100.0
"m_education"	59909.0	100.0
"source_of_lighting"	59909.0	100.0
"days_absent"	59909.0	100.0
"repeated_grades"	59909.0	100.0
"sitting_place"	59909.0	100.0
"age"	59909.0	100.0
"country"	59909.0	100.0
"socio_eco_statut"	59851.0	99.903
"student_score"	59829.0	99.866
"teacher_year_teaching"	59728.0	99.698
"f_education"	59618.0	99.514
"teacher_score"	53527.0	89.347

Rows: 1-16 | Columns: 3

We’ll simply drop the missing values to avoid adding bias to the data.

[3]:

africa.dropna()

6722 elements were filtered.

[3]:

	123 student_score Float(22)	123 teacher_score Float(22)	123 teacher_year_teaching Numeric(9)	123 number_students_school Integer	Abc english_at_home Varchar(32)	Abc travel_distance Varchar(22)	Abc means_of_travel Varchar(26)	Abc Varchar(68)	Abc Varchar(68)	Abc source_of_lighting Varchar(24)	123 days_absent Integer	Abc repeated_grades Varchar(20)	Abc sitting_place Varchar(54)	123 age Integer	123 socio_eco_statut Numeric(9)	Abc country Varchar(24)
1	425.993367323877	581.994282503848	10.0	23	SOMETIMES	>4.5-5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Namibia
2	534.329515370892	581.994282503848	10.0	23	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	7.0	Namibia
3	536.690743411639	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia
4	569.392927563969	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	9.0	Namibia
5	542.037992351316	581.994282503848	10.0	23	MOST OF THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	11.0	Namibia
6	573.771789981159	581.994282503848	10.0	23	MOST OF THE TIME	>1.5-2KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	11.0	Namibia
7	589.279157441376	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	12.0	Namibia
8	496.740841813343	581.994282503848	10.0	23	SOMETIMES	>2.5-3KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	14	12.0	Namibia
9	535.805274812767	601.83282358059	1.0	22	ALL THE TIME	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Mozambique
10	420.509155247374	715.046036359878	1.0	25	ALL THE TIME	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	3.0	Zanzibar
11	504.298378016207	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	3.0	Zanzibar
12	450.768711398358	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	4.0	Zanzibar
13	441.927245450751	715.046036359878	1.0	25	ALL THE TIME	>1-1.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Zanzibar
14	469.987298066451	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Zanzibar
15	445.259642792635	715.046036359878	1.0	25	ALL THE TIME	>4KM-4.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	6.0	Zanzibar
16	551.071920864503	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	6.0	Zanzibar
17	473.825234391116	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	7.0	Zanzibar
18	544.095820873929	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Zanzibar
19	564.874824604798	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	8.0	Zanzibar
20	386.940445160128	601.83282358059	11.0	23	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	3.0	Mozambique
21	458.501728934408	648.090960225876	3.0	23	SOMETIMES	>2-2.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	5.0	Mozambique
22	460.360232184133	601.83282358059	11.0	23	ALL THE TIME	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	15	7.0	Mozambique
23	457.035551231015	648.090960225876	3.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Mozambique
24	504.282977573042	648.090960225876	3.0	23	ALL THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Mozambique
25	475.872247772718	601.83282358059	11.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	16	10.0	Mozambique
26	503.899980617811	613.278135740248	3.0	7	ALL THE TIME	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	15	2.0	Mozambique
27	480.484906064866	613.278135740248	3.0	7	ALL THE TIME	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	15	3.0	Mozambique
28	516.744491629541	715.332169163869	20.0	25	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
29	394.65259093503	715.332169163869	20.0	25	NEVER	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia
30	506.128325450387	715.332169163869	20.0	25	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	7.0	Namibia
31	440.401203829463	715.332169163869	20.0	25	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	8.0	Namibia
32	453.010211603314	715.332169163869	20.0	25	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	11	8.0	Namibia
33	498.219068060275	715.332169163869	20.0	25	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	11.0	Namibia
34	428.988211440412	727.826634938163	8.0	23	SOMETIMES	>5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	2.0	Namibia
35	532.255684949772	727.826634938163	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	2.0	Namibia
36	392.664714363554	767.599094692976	8.0	20	ALL THE TIME	>3-3.5KM	WALK			CANDLE	0	NEVER	No place/share	13	4.0	Zambia
37	415.95588691273	727.826634938163	8.0	23	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	4.0	Namibia
38	479.525184773189	727.826634938163	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
39	410.328608434232	727.826634938163	8.0	23	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
40	425.993367323877	727.826634938163	8.0	23	SOMETIMES	>3-3.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	4.0	Namibia
41	409.430742983857	727.826634938163	8.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	5.0	Namibia
42	460.605886281468	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
43	560.188989035577	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
44	378.486087509513	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	14	6.0	Namibia
45	516.831361986859	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	6.0	Namibia
46	557.155342162198	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
47	631.282997954796	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
48	501.677328837489	727.826634938163	8.0	23	SOMETIMES	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	18	6.0	Namibia
49	466.248533790025	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
50	594.667991916549	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
51	619.020904331767	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
52	422.517903579997	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia
53	514.338009258817	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	6.0	Namibia
54	512.766872215611	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
55	456.266205420931	767.599094692976	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Zambia
56	380.388263378723	727.826634938163	8.0	23	SOMETIMES	>5KM	CAR			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	8.0	Namibia
57	421.344721387902	767.599094692976	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	11	8.0	Zambia
58	486.501284763764	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	9.0	Namibia
59	453.357504553945	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	9.0	Namibia
60	498.219068060275	691.392391229917	6.0	24	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	9.0	Namibia
61	514.807687171462	691.392391229917	6.0	24	NEVER	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	10.0	Namibia
62	565.065579807459	781.810357291219	12.0	21	MOST OF THE TIME	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	13.0	South Africa
63	626.714865963592	691.392391229917	8.0	21	ALL THE TIME	UP TO 0.5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	11	14.0	South Africa
64	457.134154158281	781.810357291219	12.0	21	SOMETIMES	>5KM	BUS/TRUCK/VAN			ELECTRIC	0	NEVER	I have my own sitting place	13	14.0	South Africa
65	510.499756960558	668.40638930927	9.0	20	MOST OF THE TIME	>1-1.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	16	2.0	Uganda
66	494.235377715545	668.40638930927	9.0	20	SOMETIMES	>1.5-2KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	17	2.0	Uganda
67	365.266644239282	635.405739248921	1.0	13	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	2.0	Zambia
68	541.173490674172	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	3.0	Namibia
69	455.36049792936	691.392391229917	8.0	20	SOMETIMES	>5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	15	3.0	Malawi
70	422.517903579997	691.392391229917	8.0	20	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	12	5.0	Malawi
71	398.31103066659	703.219213794897	1.0	21	MOST OF THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Malawi
72	395.120560563494	679.756323867598	1.0	22	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia
73	503.716941803917	691.392391229917	6.0	49	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
74	427.462485792718	646.278785800597	8.0	18	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	13	6.0	Zambia
75	600.91272658553	691.392391229917	6.0	49	SOMETIMES	>2-2.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
76	565.065579807459	691.392391229917	6.0	49	SOMETIMES	>5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
77	540.204883338675	691.392391229917	6.0	49	MOST OF THE TIME	>2.5-3KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Namibia
78	558.474690429794	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	7.0	Namibia
79	575.637662232951	691.392391229917	6.0	49	NEVER	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Namibia
80	439.680053114802	691.392391229917	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Malawi
81	353.773643278958	635.405739248921	1.0	13	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Zambia
82	488.376137298698	691.392391229917	6.0	49	SOMETIMES	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Namibia
83	480.908033418792	691.392391229917	6.0	49	MOST OF THE TIME	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia
84	535.286927844308	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia
85	408.529715955022	703.219213794897	1.0	21	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	15	9.0	Malawi
86	385.53865385057	646.278785800597	8.0	18	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	9.0	Zambia
87	528.310827853733	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	10.0	Namibia
88	548.67653911654	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	10.0	Namibia
89	588.423257247566	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Namibia
90	583.034422772394	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Namibia
91	455.36049792936	691.392391229917	8.0	20	NEVER	>3.5-4KM	WALK			ELECTRIC	0	NEVER	No place/share	14	10.0	Malawi
92	459.986311593889	691.392391229917	6.0	49	SOMETIMES	>2.5-3KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	11.0	Namibia
93	594.667991916549	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	12.0	Namibia
94	473.481862461084	691.392391229917	6.0	49	NEVER	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	12.0	Namibia
95	584.081078168864	691.392391229917	6.0	49	MOST OF THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	13.0	Namibia
96	504.241138890166	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	13.0	Namibia
97	451.694405556509	648.090960225876	7.0	15	SOMETIMES	UP TO 0.5KM	WALK			FIRE	0	NEVER	No place/share	17	1.0	Mozambique
98	522.558825103114	648.090960225876	7.0	15	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	12	1.0	Mozambique
99	422.842681154036	648.090960225876	7.0	15	NEVER	>0.5-1KM	WALK			NO LIGHTING	0	NEVER	No place/share	14	1.0	Mozambique
100	515.308862586361	709.132625077388	5.0	20	SOMETIMES	>1-1.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	18	2.0	Mozambique

Rows: 1-100 of 53187 | Columns: 16

We need to encode the categorical columns to dummies to retain linearity.

[4]:

africa.one_hot_encode(max_cardinality = 20)

/opt/venv/lib/python3.10/site-packages/verticapy/core/vdataframe/_encoding.py:123: Warning: The vDataColumn '"student_score"' was ignored because of its high cardinality.
Increase the parameter 'max_cardinality' to solve this issue or use directly the vDataColumn get_dummies method.
warnings.warn(warning_message, Warning)
/opt/venv/lib/python3.10/site-packages/verticapy/core/vdataframe/_encoding.py:123: Warning: The vDataColumn '"teacher_score"' was ignored because of its high cardinality.
Increase the parameter 'max_cardinality' to solve this issue or use directly the vDataColumn get_dummies method.
warnings.warn(warning_message, Warning)
/opt/venv/lib/python3.10/site-packages/verticapy/core/vdataframe/_encoding.py:123: Warning: The vDataColumn '"teacher_year_teaching"' was ignored because of its high cardinality.
Increase the parameter 'max_cardinality' to solve this issue or use directly the vDataColumn get_dummies method.
warnings.warn(warning_message, Warning)
/opt/venv/lib/python3.10/site-packages/verticapy/core/vdataframe/_encoding.py:123: Warning: The vDataColumn '"number_students_school"' was ignored because of its high cardinality.
Increase the parameter 'max_cardinality' to solve this issue or use directly the vDataColumn get_dummies method.
warnings.warn(warning_message, Warning)
/opt/venv/lib/python3.10/site-packages/verticapy/core/vdataframe/_encoding.py:123: Warning: The vDataColumn '"days_absent"' was ignored because of its high cardinality.
Increase the parameter 'max_cardinality' to solve this issue or use directly the vDataColumn get_dummies method.
warnings.warn(warning_message, Warning)

[4]:

	123 student_score Float(22)	123 teacher_score Float(22)	123 teacher_year_teaching Numeric(9)	123 number_students_school Integer	Abc english_at_home Varchar(32)	Abc travel_distance Varchar(22)	Abc means_of_travel Varchar(26)	Abc Varchar(68)	Abc Varchar(68)	Abc source_of_lighting Varchar(24)	123 days_absent Integer	Abc repeated_grades Varchar(20)	Abc sitting_place Varchar(54)	123 age Integer	123 socio_eco_statut Numeric(9)	Abc country Varchar(24)	123 english_at_home_ALL_THE_TIME Integer	123 english_at_home_MOST_OF_THE_TIME Integer	123 english_at_home_NEVER Integer	123 travel_distance_>0.5-1KM Integer	123 travel_distance_>1-1.5KM Integer	123 travel_distance_>1.5-2KM Integer	123 travel_distance_>2-2.5KM Integer	123 travel_distance_>2.5-3KM Integer	123 travel_distance_>3-3.5KM Integer	...	123 socio_eco_statut_3.000 Integer	123 socio_eco_statut_4.000 Integer	123 socio_eco_statut_5.000 Integer	123 socio_eco_statut_6.000 Integer	123 socio_eco_statut_7.000 Integer	123 socio_eco_statut_8.000 Integer	123 socio_eco_statut_9.000 Integer	123 socio_eco_statut_10.000 Integer	123 socio_eco_statut_11.000 Integer	123 socio_eco_statut_12.000 Integer	123 socio_eco_statut_13.000 Integer	123 socio_eco_statut_14.000 Integer	123 country_Botswana Integer	123 country_Kenya Integer	123 country_Lesotho Integer	123 country_Malawi Integer	123 country_Mozambique Integer	123 country_Namibia Integer	123 country_Seychelles Integer	123 country_South_Africa Integer	123 country_Swaziland Integer	123 country_Tanzania Integer	123 country_Uganda Integer	123 country_Zambia Integer	123 country_Zanzibar Integer
1	425.993367323877	581.994282503848	10.0	23	SOMETIMES	>4.5-5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
2	534.329515370892	581.994282503848	10.0	23	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	7.0	Namibia	0	0	0	1	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
3	536.690743411639	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
4	569.392927563969	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	9.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
5	542.037992351316	581.994282503848	10.0	23	MOST OF THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	11.0	Namibia	0	1	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
6	573.771789981159	581.994282503848	10.0	23	MOST OF THE TIME	>1.5-2KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	11.0	Namibia	0	1	0	0	0	1	0	0	0	...	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
7	589.279157441376	581.994282503848	10.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	12.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
8	496.740841813343	581.994282503848	10.0	23	SOMETIMES	>2.5-3KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	14	12.0	Namibia	0	0	0	0	0	0	0	1	0	...	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
9	535.805274812767	601.83282358059	1.0	22	ALL THE TIME	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Mozambique	1	0	0	0	1	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
10	420.509155247374	715.046036359878	1.0	25	ALL THE TIME	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	3.0	Zanzibar	1	0	0	0	0	0	0	0	0	...	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
11	504.298378016207	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	3.0	Zanzibar	1	0	0	1	0	0	0	0	0	...	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
12	450.768711398358	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	4.0	Zanzibar	1	0	0	1	0	0	0	0	0	...	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
13	441.927245450751	715.046036359878	1.0	25	ALL THE TIME	>1-1.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Zanzibar	1	0	0	0	1	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
14	469.987298066451	715.046036359878	1.0	25	ALL THE TIME	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Zanzibar	1	0	0	1	0	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
15	445.259642792635	715.046036359878	1.0	25	ALL THE TIME	>4KM-4.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	6.0	Zanzibar	1	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
16	551.071920864503	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	6.0	Zanzibar	1	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
17	473.825234391116	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	7.0	Zanzibar	1	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
18	544.095820873929	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Zanzibar	1	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
19	564.874824604798	715.046036359878	1.0	25	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	8.0	Zanzibar	1	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
20	386.940445160128	601.83282358059	11.0	23	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	3.0	Mozambique	0	0	0	1	0	0	0	0	0	...	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
21	458.501728934408	648.090960225876	3.0	23	SOMETIMES	>2-2.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	5.0	Mozambique	0	0	0	0	0	0	1	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
22	460.360232184133	601.83282358059	11.0	23	ALL THE TIME	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	15	7.0	Mozambique	1	0	0	0	0	1	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
23	457.035551231015	648.090960225876	3.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Mozambique	0	0	0	0	0	1	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
24	504.282977573042	648.090960225876	3.0	23	ALL THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Mozambique	1	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
25	475.872247772718	601.83282358059	11.0	23	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	16	10.0	Mozambique	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
26	503.899980617811	613.278135740248	3.0	7	ALL THE TIME	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	15	2.0	Mozambique	1	0	0	1	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
27	480.484906064866	613.278135740248	3.0	7	ALL THE TIME	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	15	3.0	Mozambique	1	0	0	0	0	0	0	1	0	...	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
28	516.744491629541	715.332169163869	20.0	25	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	1	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
29	394.65259093503	715.332169163869	20.0	25	NEVER	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	1	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
30	506.128325450387	715.332169163869	20.0	25	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	7.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
31	440.401203829463	715.332169163869	20.0	25	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	8.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
32	453.010211603314	715.332169163869	20.0	25	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	11	8.0	Namibia	0	0	0	1	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
33	498.219068060275	715.332169163869	20.0	25	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	11.0	Namibia	0	0	0	0	1	0	0	0	0	...	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
34	428.988211440412	727.826634938163	8.0	23	SOMETIMES	>5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	2.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
35	532.255684949772	727.826634938163	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	2.0	Namibia	0	0	0	1	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
36	392.664714363554	767.599094692976	8.0	20	ALL THE TIME	>3-3.5KM	WALK			CANDLE	0	NEVER	No place/share	13	4.0	Zambia	1	0	0	0	0	0	0	0	1	...	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
37	415.95588691273	727.826634938163	8.0	23	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	4.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
38	479.525184773189	727.826634938163	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia	0	0	0	1	0	0	0	0	0	...	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
39	410.328608434232	727.826634938163	8.0	23	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia	0	0	0	0	1	0	0	0	0	...	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
40	425.993367323877	727.826634938163	8.0	23	SOMETIMES	>3-3.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	4.0	Namibia	0	0	0	0	0	0	0	0	1	...	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
41	409.430742983857	727.826634938163	8.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	5.0	Namibia	0	0	0	0	0	1	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
42	460.605886281468	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
43	560.188989035577	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
44	378.486087509513	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	14	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
45	516.831361986859	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
46	557.155342162198	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
47	631.282997954796	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
48	501.677328837489	727.826634938163	8.0	23	SOMETIMES	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	18	6.0	Namibia	0	0	0	0	0	0	0	1	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
49	466.248533790025	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
50	594.667991916549	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
51	619.020904331767	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
52	422.517903579997	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
53	514.338009258817	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
54	512.766872215611	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
55	456.266205420931	767.599094692976	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Zambia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
56	380.388263378723	727.826634938163	8.0	23	SOMETIMES	>5KM	CAR			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	8.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
57	421.344721387902	767.599094692976	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	11	8.0	Zambia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
58	486.501284763764	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	9.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
59	453.357504553945	691.392391229917	6.0	24	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	9.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
60	498.219068060275	691.392391229917	6.0	24	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	9.0	Namibia	0	0	0	1	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
61	514.807687171462	691.392391229917	6.0	24	NEVER	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	10.0	Namibia	0	0	1	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
62	565.065579807459	781.810357291219	12.0	21	MOST OF THE TIME	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	13.0	South Africa	0	1	0	1	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0
63	626.714865963592	691.392391229917	8.0	21	ALL THE TIME	UP TO 0.5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	11	14.0	South Africa	1	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0
64	457.134154158281	781.810357291219	12.0	21	SOMETIMES	>5KM	BUS/TRUCK/VAN			ELECTRIC	0	NEVER	I have my own sitting place	13	14.0	South Africa	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0
65	510.499756960558	668.40638930927	9.0	20	MOST OF THE TIME	>1-1.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	16	2.0	Uganda	0	1	0	0	1	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
66	494.235377715545	668.40638930927	9.0	20	SOMETIMES	>1.5-2KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	17	2.0	Uganda	0	0	0	0	0	1	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
67	365.266644239282	635.405739248921	1.0	13	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	2.0	Zambia	0	0	1	1	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
68	541.173490674172	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	3.0	Namibia	0	0	0	0	0	0	0	0	0	...	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
69	455.36049792936	691.392391229917	8.0	20	SOMETIMES	>5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	15	3.0	Malawi	0	0	0	0	0	0	0	0	0	...	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
70	422.517903579997	691.392391229917	8.0	20	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	12	5.0	Malawi	0	0	1	1	0	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
71	398.31103066659	703.219213794897	1.0	21	MOST OF THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	14	5.0	Malawi	0	1	0	0	0	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
72	395.120560563494	679.756323867598	1.0	22	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
73	503.716941803917	691.392391229917	6.0	49	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
74	427.462485792718	646.278785800597	8.0	18	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	13	6.0	Zambia	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
75	600.91272658553	691.392391229917	6.0	49	SOMETIMES	>2-2.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia	0	0	0	0	0	0	1	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
76	565.065579807459	691.392391229917	6.0	49	SOMETIMES	>5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
77	540.204883338675	691.392391229917	6.0	49	MOST OF THE TIME	>2.5-3KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Namibia	0	1	0	0	0	0	0	1	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
78	558.474690429794	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	7.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
79	575.637662232951	691.392391229917	6.0	49	NEVER	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Namibia	0	0	1	1	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
80	439.680053114802	691.392391229917	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Malawi	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
81	353.773643278958	635.405739248921	1.0	13	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Zambia	0	0	0	1	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
82	488.376137298698	691.392391229917	6.0	49	SOMETIMES	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Namibia	0	0	0	0	1	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
83	480.908033418792	691.392391229917	6.0	49	MOST OF THE TIME	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia	0	1	0	0	1	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
84	535.286927844308	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	8.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
85	408.529715955022	703.219213794897	1.0	21	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	15	9.0	Malawi	0	0	0	1	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
86	385.53865385057	646.278785800597	8.0	18	SOMETIMES	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	9.0	Zambia	0	0	0	1	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
87	528.310827853733	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	10.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
88	548.67653911654	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	10.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
89	588.423257247566	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
90	583.034422772394	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	10.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
91	455.36049792936	691.392391229917	8.0	20	NEVER	>3.5-4KM	WALK			ELECTRIC	0	NEVER	No place/share	14	10.0	Malawi	0	0	1	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
92	459.986311593889	691.392391229917	6.0	49	SOMETIMES	>2.5-3KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	11.0	Namibia	0	0	0	0	0	0	0	1	0	...	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
93	594.667991916549	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	12.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
94	473.481862461084	691.392391229917	6.0	49	NEVER	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	12.0	Namibia	0	0	1	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
95	584.081078168864	691.392391229917	6.0	49	MOST OF THE TIME	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	13.0	Namibia	0	1	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0
96	504.241138890166	691.392391229917	6.0	49	SOMETIMES	UP TO 0.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	13.0	Namibia	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0
97	451.694405556509	648.090960225876	7.0	15	SOMETIMES	UP TO 0.5KM	WALK			FIRE	0	NEVER	No place/share	17	1.0	Mozambique	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
98	522.558825103114	648.090960225876	7.0	15	ALL THE TIME	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	12	1.0	Mozambique	1	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
99	422.842681154036	648.090960225876	7.0	15	NEVER	>0.5-1KM	WALK			NO LIGHTING	0	NEVER	No place/share	14	1.0	Mozambique	0	0	1	1	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
100	515.308862586361	709.132625077388	5.0	20	SOMETIMES	>1-1.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	18	2.0	Mozambique	0	0	0	0	1	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0

Rows: 1-100 of 53187 | Columns: 51

Linear regression can only handle numerical columns, so we’ll drop the categorical columns.

[5]:

africa.drop(columns = ["english_at_home",
                       "travel_distance",
                       "means_of_travel",
                       "m_education",
                       "f_education",
                       "source_of_lighting",
                       "repeated_grades",
                       "sitting_place",
                       "country"])

[5]:

	123 student_score Float(22)	123 teacher_score Float(22)	123 teacher_year_teaching Numeric(9)	123 number_students_school Integer	123 days_absent Integer	123 age Integer	123 socio_eco_statut Numeric(9)	123 english_at_home_ALL_THE_TIME Integer	123 english_at_home_MOST_OF_THE_TIME Integer	123 english_at_home_NEVER Integer	123 travel_distance_>0.5-1KM Integer	123 travel_distance_>1-1.5KM Integer	123 travel_distance_>1.5-2KM Integer	123 travel_distance_>2-2.5KM Integer	123 travel_distance_>2.5-3KM Integer	123 travel_distance_>3-3.5KM Integer	123 travel_distance_>3.5-4KM Integer	123 travel_distance_>4.5-5KM Integer	123 travel_distance_>4KM-4.5KM Integer	123 travel_distance_>5KM Integer	123 means_of_travel_BICYCLE Integer	123 means_of_travel_BUS_TRUCK_VAN Integer	123 means_of_travel_CAR Integer	123 means_of_travel_OTHER Integer	123 means_of_travel_TRAIN Integer	...	123 socio_eco_statut_3.000 Integer	123 socio_eco_statut_4.000 Integer	123 socio_eco_statut_5.000 Integer	123 socio_eco_statut_6.000 Integer	123 socio_eco_statut_7.000 Integer	123 socio_eco_statut_8.000 Integer	123 socio_eco_statut_9.000 Integer	123 socio_eco_statut_10.000 Integer	123 socio_eco_statut_11.000 Integer	123 socio_eco_statut_12.000 Integer	123 socio_eco_statut_13.000 Integer	123 socio_eco_statut_14.000 Integer	123 country_Botswana Integer	123 country_Kenya Integer	123 country_Lesotho Integer	123 country_Malawi Integer	123 country_Mozambique Integer	123 country_Namibia Integer	123 country_Seychelles Integer	123 country_South_Africa Integer	123 country_Swaziland Integer	123 country_Tanzania Integer	123 country_Uganda Integer	123 country_Zambia Integer	123 country_Zanzibar Integer
1	425.993367323877	581.994282503848	10.0	23	0	14	5.0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
2	534.329515370892	581.994282503848	10.0	23	0	13	7.0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
3	536.690743411639	581.994282503848	10.0	23	0	12	8.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
4	569.392927563969	581.994282503848	10.0	23	0	13	9.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
5	542.037992351316	581.994282503848	10.0	23	0	12	11.0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
6	573.771789981159	581.994282503848	10.0	23	0	12	11.0	0	1	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	...	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
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70	422.517903579997	691.392391229917	8.0	20	0	12	5.0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
71	398.31103066659	703.219213794897	1.0	21	0	14	5.0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
72	395.120560563494	679.756323867598	1.0	22	0	12	6.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
73	503.716941803917	691.392391229917	6.0	49	0	12	6.0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
74	427.462485792718	646.278785800597	8.0	18	0	13	6.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
75	600.91272658553	691.392391229917	6.0	49	0	12	7.0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
76	565.065579807459	691.392391229917	6.0	49	0	12	7.0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	1	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
77	540.204883338675	691.392391229917	6.0	49	0	11	7.0	0	1	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
78	558.474690429794	691.392391229917	6.0	49	0	12	7.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
79	575.637662232951	691.392391229917	6.0	49	0	13	7.0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
80	439.680053114802	691.392391229917	8.0	20	0	11	7.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
81	353.773643278958	635.405739248921	1.0	13	0	13	7.0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
82	488.376137298698	691.392391229917	6.0	49	0	11	8.0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
83	480.908033418792	691.392391229917	6.0	49	0	12	8.0	0	1	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
84	535.286927844308	691.392391229917	6.0	49	0	12	8.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
85	408.529715955022	703.219213794897	1.0	21	0	15	9.0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
86	385.53865385057	646.278785800597	8.0	18	0	12	9.0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
87	528.310827853733	691.392391229917	6.0	49	0	12	10.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
88	548.67653911654	691.392391229917	6.0	49	0	12	10.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
89	588.423257247566	691.392391229917	6.0	49	0	13	10.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
90	583.034422772394	691.392391229917	6.0	49	0	13	10.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
91	455.36049792936	691.392391229917	8.0	20	0	14	10.0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
92	459.986311593889	691.392391229917	6.0	49	0	13	11.0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
93	594.667991916549	691.392391229917	6.0	49	0	12	12.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
94	473.481862461084	691.392391229917	6.0	49	0	11	12.0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
95	584.081078168864	691.392391229917	6.0	49	0	12	13.0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0
96	504.241138890166	691.392391229917	6.0	49	0	11	13.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0
97	451.694405556509	648.090960225876	7.0	15	0	17	1.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
98	522.558825103114	648.090960225876	7.0	15	0	12	1.0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
99	422.842681154036	648.090960225876	7.0	15	0	14	1.0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
100	515.308862586361	709.132625077388	5.0	20	0	18	2.0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0

Rows: 1-100 of 53187 | Columns: 50

Let’s look at the correlation between the response column and the predictors. We’ll look to keep columns with correlations coefficients greater than 20% (the top 10 features).

[6]:

x = africa.corr(focus = "student_score", show = False)

[7]:

africa = africa.select(columns = x["index"][0:12])
display(africa)

	123 student_score Float(22)	123 socio_eco_statut Numeric(9)	123 source_of_lighting_ELECTRIC Integer	123 means_of_travel_CAR Integer	123 socio_eco_statut_14.000 Integer	123 repeated_grades_NEVER Integer	123 english_at_home_NEVER Integer	123 age Integer	123 country_Tanzania Integer	123 teacher_score Float(22)	123 source_of_lighting_CANDLE Integer	123 Integer
1	425.993367323877	5.0	0	0	0	1	0	14	0	581.994282503848	0
2	534.329515370892	7.0	1	0	0	1	0	13	0	581.994282503848	0
3	536.690743411639	8.0	1	0	0	1	0	12	0	581.994282503848	0
4	569.392927563969	9.0	1	0	0	1	0	13	0	581.994282503848	0
5	542.037992351316	11.0	1	0	0	1	0	12	0	581.994282503848	0
6	573.771789981159	11.0	1	1	0	1	0	12	0	581.994282503848	0
7	589.279157441376	12.0	1	0	0	1	0	12	0	581.994282503848	0
8	496.740841813343	12.0	1	1	0	1	0	14	0	581.994282503848	0
9	535.805274812767	10.0	1	0	0	1	0	13	0	601.83282358059	0
10	420.509155247374	3.0	0	0	0	1	0	13	0	715.046036359878	0
11	504.298378016207	3.0	0	0	0	1	0	13	0	715.046036359878	0
12	450.768711398358	4.0	0	0	0	1	0	14	0	715.046036359878	0
13	441.927245450751	5.0	0	0	0	1	0	14	0	715.046036359878	0
14	469.987298066451	5.0	0	0	0	1	0	14	0	715.046036359878	0
15	445.259642792635	6.0	0	0	0	1	0	13	0	715.046036359878	0
16	551.071920864503	6.0	0	0	0	1	0	13	0	715.046036359878	0
17	473.825234391116	7.0	0	0	0	1	0	12	0	715.046036359878	0
18	544.095820873929	8.0	1	0	0	1	0	12	0	715.046036359878	0
19	564.874824604798	8.0	0	0	0	1	0	14	0	715.046036359878	0
20	386.940445160128	3.0	0	0	0	1	0	14	0	601.83282358059	0
21	458.501728934408	5.0	0	0	0	1	0	14	0	648.090960225876	1
22	460.360232184133	7.0	1	0	0	1	0	15	0	601.83282358059	0
23	457.035551231015	7.0	1	0	0	1	0	11	0	648.090960225876	0
24	504.282977573042	8.0	1	0	0	1	0	11	0	648.090960225876	0
25	475.872247772718	10.0	1	0	0	1	0	16	0	601.83282358059	0
26	503.899980617811	2.0	0	0	0	1	0	15	0	613.278135740248	1
27	480.484906064866	3.0	0	0	0	1	0	15	0	613.278135740248	1
28	516.744491629541	6.0	0	0	0	1	0	12	0	715.332169163869	1
29	394.65259093503	6.0	0	0	0	1	1	12	0	715.332169163869	0
30	506.128325450387	7.0	0	0	0	1	0	11	0	715.332169163869	1
31	440.401203829463	8.0	0	0	0	1	0	12	0	715.332169163869	0
32	453.010211603314	8.0	0	0	0	1	0	11	0	715.332169163869	0
33	498.219068060275	11.0	0	0	0	1	0	11	0	715.332169163869	1
34	428.988211440412	2.0	0	0	0	1	0	12	0	727.826634938163	0
35	532.255684949772	2.0	0	0	0	1	0	14	0	727.826634938163	1
36	392.664714363554	4.0	0	0	0	1	0	13	0	767.599094692976	1
37	415.95588691273	4.0	0	0	0	1	0	13	0	727.826634938163	1
38	479.525184773189	4.0	0	0	0	1	0	12	0	727.826634938163	1
39	410.328608434232	4.0	0	0	0	1	0	12	0	727.826634938163	1
40	425.993367323877	4.0	0	0	0	1	0	12	0	727.826634938163	0
41	409.430742983857	5.0	1	0	0	1	0	12	0	727.826634938163	0
42	460.605886281468	6.0	1	0	0	1	0	12	0	691.392391229917	0
43	560.188989035577	6.0	1	0	0	1	0	12	0	691.392391229917	0
44	378.486087509513	6.0	1	0	0	1	0	14	0	691.392391229917	0
45	516.831361986859	6.0	1	0	0	1	0	11	0	691.392391229917	0
46	557.155342162198	6.0	1	0	0	1	0	12	0	691.392391229917	0
47	631.282997954796	6.0	1	0	0	1	0	12	0	691.392391229917	0
48	501.677328837489	6.0	0	0	0	1	0	18	0	727.826634938163	1
49	466.248533790025	6.0	1	0	0	1	0	12	0	691.392391229917	0
50	594.667991916549	6.0	1	0	0	1	0	12	0	691.392391229917	0
51	619.020904331767	6.0	1	0	0	1	0	12	0	691.392391229917	0
52	422.517903579997	6.0	1	0	0	1	0	12	0	691.392391229917	0
53	514.338009258817	6.0	1	0	0	1	0	11	0	691.392391229917	0
54	512.766872215611	7.0	1	0	0	1	0	12	0	691.392391229917	0
55	456.266205420931	7.0	0	0	0	1	0	11	0	767.599094692976	1
56	380.388263378723	8.0	0	1	0	1	0	13	0	727.826634938163	0
57	421.344721387902	8.0	0	0	0	1	0	11	0	767.599094692976	0
58	486.501284763764	9.0	1	0	0	1	0	13	0	691.392391229917	0
59	453.357504553945	9.0	1	0	0	1	0	12	0	691.392391229917	0
60	498.219068060275	9.0	1	0	0	1	0	11	0	691.392391229917	0
61	514.807687171462	10.0	1	0	0	1	1	12	0	691.392391229917	0
62	565.065579807459	13.0	1	0	0	1	0	12	0	781.810357291219	0
63	626.714865963592	14.0	1	1	1	1	0	11	0	691.392391229917	0
64	457.134154158281	14.0	1	0	1	1	0	13	0	781.810357291219	0
65	510.499756960558	2.0	0	0	0	1	0	16	0	668.40638930927	0
66	494.235377715545	2.0	0	0	0	1	0	17	0	668.40638930927	0
67	365.266644239282	2.0	0	0	0	1	1	13	0	635.405739248921	0
68	541.173490674172	3.0	1	0	0	1	0	12	0	691.392391229917	0
69	455.36049792936	3.0	0	0	0	1	0	15	0	691.392391229917	0
70	422.517903579997	5.0	0	0	0	1	1	12	0	691.392391229917	0
71	398.31103066659	5.0	0	0	0	1	0	14	0	703.219213794897	0
72	395.120560563494	6.0	0	0	0	1	0	12	0	679.756323867598	0
73	503.716941803917	6.0	0	0	0	1	0	12	0	691.392391229917	1
74	427.462485792718	6.0	0	0	0	1	0	13	0	646.278785800597	1
75	600.91272658553	7.0	1	0	0	1	0	12	0	691.392391229917	0
76	565.065579807459	7.0	1	1	0	1	0	12	0	691.392391229917	0
77	540.204883338675	7.0	1	0	0	1	0	11	0	691.392391229917	0
78	558.474690429794	7.0	0	0	0	1	0	12	0	691.392391229917	0
79	575.637662232951	7.0	0	0	0	1	1	13	0	691.392391229917	1
80	439.680053114802	7.0	0	0	0	1	0	11	0	691.392391229917	1
81	353.773643278958	7.0	0	0	0	1	0	13	0	635.405739248921	1
82	488.376137298698	8.0	1	0	0	1	0	11	0	691.392391229917	0
83	480.908033418792	8.0	1	0	0	1	0	12	0	691.392391229917	0
84	535.286927844308	8.0	1	0	0	1	0	12	0	691.392391229917	0
85	408.529715955022	9.0	0	0	0	1	0	15	0	703.219213794897	0
86	385.53865385057	9.0	0	0	0	1	0	12	0	646.278785800597	0
87	528.310827853733	10.0	0	0	0	1	0	12	0	691.392391229917	0
88	548.67653911654	10.0	1	0	0	1	0	12	0	691.392391229917	0
89	588.423257247566	10.0	1	0	0	1	0	13	0	691.392391229917	0
90	583.034422772394	10.0	1	0	0	1	0	13	0	691.392391229917	0
91	455.36049792936	10.0	1	0	0	1	1	14	0	691.392391229917	0
92	459.986311593889	11.0	1	0	0	1	0	13	0	691.392391229917	0
93	594.667991916549	12.0	1	0	0	1	0	12	0	691.392391229917	0
94	473.481862461084	12.0	1	0	0	1	1	11	0	691.392391229917	0
95	584.081078168864	13.0	1	0	0	1	0	12	0	691.392391229917	0
96	504.241138890166	13.0	1	0	0	1	0	11	0	691.392391229917	0
97	451.694405556509	1.0	0	0	0	1	0	17	0	648.090960225876	0
98	522.558825103114	1.0	0	0	0	1	0	12	0	648.090960225876	0
99	422.842681154036	1.0	0	0	0	1	1	14	0	648.090960225876	0
100	515.308862586361	2.0	0	0	0	1	0	18	0	709.132625077388	0

Rows: 1-100 | Columns: 12

Let’s examine the correlation matrix to see if we have any independent predictors.

[8]:

africa.corr()

[8]:

Some of these features are highly-correlated, like socioeconomic status and having an electric lighting. We’ll drop the lighting column to avoid unexpected results while computing the linear regression.

[9]:

africa["source_of_lighting_ELECTRIC"].drop()

[9]:

	123 student_score Float(22)	123 socio_eco_statut Numeric(9)	123 means_of_travel_CAR Integer	123 socio_eco_statut_14.000 Integer	123 repeated_grades_NEVER Integer	123 english_at_home_NEVER Integer	123 age Integer	123 country_Tanzania Integer	123 teacher_score Float(22)	123 source_of_lighting_CANDLE Integer	123 Integer
1	425.993367323877	5.0	0	0	1	0	14	0	581.994282503848	0
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20	386.940445160128	3.0	0	0	1	0	14	0	601.83282358059	0
21	458.501728934408	5.0	0	0	1	0	14	0	648.090960225876	1
22	460.360232184133	7.0	0	0	1	0	15	0	601.83282358059	0
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25	475.872247772718	10.0	0	0	1	0	16	0	601.83282358059	0
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74	427.462485792718	6.0	0	0	1	0	13	0	646.278785800597	1
75	600.91272658553	7.0	0	0	1	0	12	0	691.392391229917	0
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78	558.474690429794	7.0	0	0	1	0	12	0	691.392391229917	0
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80	439.680053114802	7.0	0	0	1	0	11	0	691.392391229917	1
81	353.773643278958	7.0	0	0	1	0	13	0	635.405739248921	1
82	488.376137298698	8.0	0	0	1	0	11	0	691.392391229917	0
83	480.908033418792	8.0	0	0	1	0	12	0	691.392391229917	0
84	535.286927844308	8.0	0	0	1	0	12	0	691.392391229917	0
85	408.529715955022	9.0	0	0	1	0	15	0	703.219213794897	0
86	385.53865385057	9.0	0	0	1	0	12	0	646.278785800597	0
87	528.310827853733	10.0	0	0	1	0	12	0	691.392391229917	0
88	548.67653911654	10.0	0	0	1	0	12	0	691.392391229917	0
89	588.423257247566	10.0	0	0	1	0	13	0	691.392391229917	0
90	583.034422772394	10.0	0	0	1	0	13	0	691.392391229917	0
91	455.36049792936	10.0	0	0	1	1	14	0	691.392391229917	0
92	459.986311593889	11.0	0	0	1	0	13	0	691.392391229917	0
93	594.667991916549	12.0	0	0	1	0	12	0	691.392391229917	0
94	473.481862461084	12.0	0	0	1	1	11	0	691.392391229917	0
95	584.081078168864	13.0	0	0	1	0	12	0	691.392391229917	0
96	504.241138890166	13.0	0	0	1	0	11	0	691.392391229917	0
97	451.694405556509	1.0	0	0	1	0	17	0	648.090960225876	0
98	522.558825103114	1.0	0	0	1	0	12	0	648.090960225876	0
99	422.842681154036	1.0	0	0	1	1	14	0	648.090960225876	0
100	515.308862586361	2.0	0	0	1	0	18	0	709.132625077388	0

Rows: 1-100 | Columns: 11

Let’s normalize the dataset to follow the Gaussian-Markov assumptions.

[10]:

africa.normalize(columns = africa.get_columns(exclude_columns = ["student_score"]))

[10]:

	123 student_score Float(22)	123 socio_eco_statut Numeric(49)	123 means_of_travel_CAR Numeric(66)	123 socio_eco_statut_14.000 Numeric(66)	123 repeated_grades_NEVER Numeric(65)	123 english_at_home_NEVER Numeric(65)	123 age Numeric(62)	123 country_Tanzania Numeric(65)	123 teacher_score Float(22)	123 source_of_lighting_CANDLE Numeric(65)	123 Numeric(65)
1	425.993367323877	-0.6232054442632663	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
2	534.329515370892	-0.03943601904258274	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
3	536.690743411639	0.25244869356775906	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
4	569.392927563969	0.5443334061781009	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
5	542.037992351316	1.1281028313987844	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
6	573.771789981159	1.1281028313987844	4.180166793098136	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
7	589.279157441376	1.4199875440091263	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
8	496.740841813343	1.4199875440091263	4.180166793098136	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-2.25571926837901	-0.5195382107595631
9	535.805274812767	0.8362181187884427	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-1.98588881675302	-0.5195382107595631
10	420.509155247374	-1.20697486948395	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
11	504.298378016207	-1.20697486948395	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
12	450.768711398358	-0.9150901568736081	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
13	441.927245450751	-0.6232054442632663	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
14	469.987298066451	-0.6232054442632663	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
15	445.259642792635	-0.3313207316529245	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
16	551.071920864503	-0.3313207316529245	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
17	473.825234391116	-0.03943601904258274	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
18	544.095820873929	0.25244869356775906	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
19	564.874824604798	0.25244869356775906	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-0.446039075983578	-0.5195382107595631
20	386.940445160128	-1.20697486948395	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-1.98588881675302	-0.5195382107595631
21	458.501728934408	-0.6232054442632663	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-1.35671685022128	1.9247500524574985
22	460.360232184133	-0.03943601904258274	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.9834086341847834	-0.28509087397763944	-1.98588881675302	-0.5195382107595631
23	457.035551231015	-0.03943601904258274	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-1.4088323540213517	-0.28509087397763944	-1.35671685022128	-0.5195382107595631
24	504.282977573042	0.25244869356775906	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-1.4088323540213517	-0.28509087397763944	-1.35671685022128	-0.5195382107595631
25	475.872247772718	0.8362181187884427	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	1.5814688812363171	-0.28509087397763944	-1.98588881675302	-0.5195382107595631
26	503.899980617811	-1.4988595820942916	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.9834086341847834	-0.28509087397763944	-1.83021740235342	1.9247500524574985
27	480.484906064866	-1.20697486948395	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.9834086341847834	-0.28509087397763944	-1.83021740235342	1.9247500524574985
28	516.744491629541	-0.3313207316529245	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.442147290623594	1.9247500524574985
29	394.65259093503	-0.3313207316529245	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	2.0669357515682547	-0.8107721069698178	-0.28509087397763944	-0.442147290623594	-0.5195382107595631
30	506.128325450387	-0.03943601904258274	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-1.4088323540213517	-0.28509087397763944	-0.442147290623594	1.9247500524574985
31	440.401203829463	0.25244869356775906	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.442147290623594	-0.5195382107595631
32	453.010211603314	0.25244869356775906	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-1.4088323540213517	-0.28509087397763944	-0.442147290623594	-0.5195382107595631
33	498.219068060275	1.1281028313987844	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-1.4088323540213517	-0.28509087397763944	-0.442147290623594	1.9247500524574985
34	428.988211440412	-1.4988595820942916	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.272205996570688	-0.5195382107595631
35	532.255684949772	-1.4988595820942916	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.38534838713324965	-0.28509087397763944	-0.272205996570688	1.9247500524574985
36	392.664714363554	-0.9150901568736081	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	0.268752168467943	1.9247500524574985
37	415.95588691273	-0.9150901568736081	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.272205996570688	1.9247500524574985
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72	395.120560563494	-0.3313207316529245	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.926025937049029	-0.5195382107595631
73	503.716941803917	-0.3313207316529245	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.7677599990761	1.9247500524574985
74	427.462485792718	-0.3313207316529245	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-1.38136482416788	1.9247500524574985
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80	439.680053114802	-0.03943601904258274	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-1.4088323540213517	-0.28509087397763944	-0.7677599990761	1.9247500524574985
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84	535.286927844308	0.25244869356775906	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
85	408.529715955022	0.5443334061781009	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	0.9834086341847834	-0.28509087397763944	-0.606899537529847	-0.5195382107595631
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89	588.423257247566	0.8362181187884427	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
90	583.034422772394	0.8362181187884427	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
91	455.36049792936	0.8362181187884427	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	2.0669357515682547	0.38534838713324965	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
92	459.986311593889	1.1281028313987844	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.21271185991828412	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
93	594.667991916549	1.4199875440091263	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
94	473.481862461084	1.4199875440091263	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	2.0669357515682547	-1.4088323540213517	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
95	584.081078168864	1.711872256619468	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
96	504.241138890166	1.711872256619468	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-1.4088323540213517	-0.28509087397763944	-0.7677599990761	-0.5195382107595631
97	451.694405556509	-1.7907442947046335	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	2.179529128287851	-0.28509087397763944	-1.35671685022128	-0.5195382107595631
98	522.558825103114	-1.7907442947046335	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	-0.8107721069698178	-0.28509087397763944	-1.35671685022128	-0.5195382107595631
99	422.842681154036	-1.7907442947046335	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	2.0669357515682547	0.38534838713324965	-0.28509087397763944	-1.35671685022128	-0.5195382107595631
100	515.308862586361	-1.4988595820942916	-0.23922040624412672	-0.17707300662955064	0.8056324835156974	-0.48379887843849295	2.7775893753393848	-0.28509087397763944	-0.526469306756706	-0.5195382107595631

Rows: 1-100 of 53187 | Columns: 11

We can use a cross-validation to test our model.

[11]:

from verticapy.learn.linear_model import LinearRegression
from verticapy.learn.model_selection import cross_validate
cross_validate(LinearRegression("africa_lr", solver = "BFGS"),
               input_relation = africa,
               X = africa.get_columns(exclude_columns = ["student_score"]),
               y = "student_score")

[11]:

	explained_variance	max_error	median_absolute_error	mean_absolute_error	mean_squared_error	root_mean_squared_error	r2	r2_adj	aic	bic	time
1-fold	0.298760420922965	454.869941453916	48.2210772255159	57.1543070024498	5338.63008987636	72.4282147941313	0.298760190415264	0.298365325946778	152537.040399237	152622.64984117	1.1311068534851074
2-fold	0.290976792434127	389.687661828984	48.6556666765512	57.7359307029193	5318.83475392814	73.0176869855228	0.290968638054247	0.290569857760689	152651.186957684	152736.809425035	1.0947003364562988
3-fold	0.29592130733471	455.880251469504	48.9063941477698	58.1178896758865	5331.51254823777	73.8833042681213	0.295920687999041	0.2955219569355	151646.613109167	151732.159688654	1.123023271560669
avg	0.29521950689726734	433.479284917468	48.59437934994563	57.66937579375186	5329.659130680757	73.10973534925846	0.29521650548951733	0.294819046880989	152278.28015536268	152363.872984953	1.1162768205006917
std	0.0032161686319344554	30.968100481245564	0.2831159047501379	0.3961860329757309	8.186989630147114	0.5975929608459388	0.0032196249060676588	0.003221065348465828	449.08039528091683	449.11347429334876	0.015609710054337617

Rows: 1-5 | Columns: 12

The model isn’t bad. We’re just using a few variables to get a median absolute error of 47; that is, our score has a distance of 47 from the true value. This seems high, but if we keep in mind that the final score is over 1000, our predictions are quite good.

Let’s compare the importance of our features.

[12]:

model = LinearRegression("africa_lr", solver = "BFGS")
model.fit(input_relation = africa,
          X = africa.get_columns(exclude_columns = ["student_score"]),
          y = "student_score")
x = model.features_importance()

The following factors seem to have the greatest influence on a student’s performance:

Having a good teacher
Being of good socio-economic status
Tanzanian teachers tend to overrate their students
Age (younger students tend to perform better)
Being able to get to school by car

Let’s add the prediction to the vDataFrame to see how our model performs its estimations.

[13]:

model.predict(africa, name = "estimated_student_score")
africa.boxplot(["estimated_student_score", "student_score"])

[13]:

[14]:

africa.describe(columns = ["student_score", "estimated_student_score"])

[14]:

	count	mean	std	min	approx_25%	approx_50%	approx_75%	max
"student_score"	53187	504.04486138049	86.6635761677015	117.532999839887	440.477255657786	493.341623606933	558.426056654596	943.673770012441
"estimated_student_score"	53187	504.044854820435	46.8688907816558	383.47030012421	470.524720321282	497.526659532846	532.538926505113	689.969909839223

Rows: 1-2 | Columns: 9

Our model has trouble catching outliers: exceptionally well-performing and struggling students.

Let’s draw a residual plot.

[15]:

africa["residual"] = africa["student_score"] - africa["estimated_student_score"]
africa.scatter(["residual", "student_score"])

[15]:

We see a high heteroscedasticity, indicating that we can’t trust the p-value of the coefficients.

[16]:

model.coef_

[16]:

array([ 19.98559453,   8.06019088,   6.51734115,   8.72050689,
       -12.25601014,  -5.90939743,  22.15292132,  11.14638302,
        -3.73140578,   4.90042492])

Let’s look at the model’s analysis of variance (ANOVA) table.

[17]:

model.report("anova")

[17]:

	Df	SS	MS	F	p_value
Regression	10	116833309.808147	11683330.9808147	2198.2268183057104	0.0
Residual	53176	282624524.030987	5314.888747385795
Total	53186	399457465.042041

Rows: 1-3 | Columns: 6

According to the ANOVA table, at least one of our variables is influencing the prediction.

We can also see that a student’s estimated score and true score skew heavily from a normal distribution.

[18]:

africa["estimated_student_score"].hist()

from verticapy.stats import jarque_bera
jarque_bera(africa, "estimated_student_score")

[18]:

(4001.26169047401, 0.0)

Our model doesn’t verify the basic hypothesis and therefore isn’t stable enough to be put into production. Let’s look at a second technique.

Example with decomposition#

Let’s look at the same dataset, but use decomposition techniques to filter out unimportant information. We don’t have to normalize our data or look at correlations with these types of methods.

We’ll begin by repeating the data preparation process of the previous section and export the resulting vDataFrame to Vertica.

[24]:

africa = vp.read_csv("data/africa_education.csv")
africa = africa.select(["(zralocp + zmalocp) / 2 AS student_score",
                        "zraloct AS teacher_score",
                        "XNUMYRS AS teacher_year_teaching",
                        "numstu AS number_students_school",
                        "PENGLISH AS english_at_home",
                        "PTRAVEL AS travel_distance",
                        "PTRAVEL2 AS means_of_travel",
                        "PMOTHER AS m_education",
                        "PFATHER AS f_education",
                        "PLIGHT AS source_of_lighting",
                        "PABSENT AS days_absent",
                        "PREPEAT AS repeated_grades",
                        "zpsit AS sitting_place",
                        "PAGE AS age",
                        "zpses AS socio_eco_statut",
                        "country_long AS country"])
africa.dropna()
africa.one_hot_encode(max_cardinality = 20)
africa.drop(columns = ["english_at_home",
                       "travel_distance",
                       "means_of_travel",
                       "m_education",
                       "f_education",
                       "source_of_lighting",
                       "repeated_grades",
                       "sitting_place",
                       "country"])
vp.drop("africa_clean", method = "table")
africa.to_db("africa_clean",
             relation_type = "table")

6722 elements were filtered.

[24]:

	123 student_score Float(22)	123 teacher_score Float(22)	123 teacher_year_teaching Numeric(9)	123 number_students_school Integer	123 days_absent Integer	123 age Integer	123 socio_eco_statut Numeric(9)	123 english_at_home_ALL_THE_TIME Integer	123 english_at_home_MOST_OF_THE_TIME Integer	123 english_at_home_NEVER Integer	123 travel_distance_>0.5-1KM Integer	123 travel_distance_>1-1.5KM Integer	123 travel_distance_>1.5-2KM Integer	123 travel_distance_>2-2.5KM Integer	123 travel_distance_>2.5-3KM Integer	123 travel_distance_>3-3.5KM Integer	123 travel_distance_>3.5-4KM Integer	123 travel_distance_>4.5-5KM Integer	123 travel_distance_>4KM-4.5KM Integer	123 travel_distance_>5KM Integer	123 means_of_travel_BICYCLE Integer	123 means_of_travel_BUS_TRUCK_VAN Integer	123 means_of_travel_CAR Integer	123 means_of_travel_OTHER Integer	123 means_of_travel_TRAIN Integer	...	123 socio_eco_statut_3.000 Integer	123 socio_eco_statut_4.000 Integer	123 socio_eco_statut_5.000 Integer	123 socio_eco_statut_6.000 Integer	123 socio_eco_statut_7.000 Integer	123 socio_eco_statut_8.000 Integer	123 socio_eco_statut_9.000 Integer	123 socio_eco_statut_10.000 Integer	123 socio_eco_statut_11.000 Integer	123 socio_eco_statut_12.000 Integer	123 socio_eco_statut_13.000 Integer	123 socio_eco_statut_14.000 Integer	123 country_Botswana Integer	123 country_Kenya Integer	123 country_Lesotho Integer	123 country_Malawi Integer	123 country_Mozambique Integer	123 country_Namibia Integer	123 country_Seychelles Integer	123 country_South_Africa Integer	123 country_Swaziland Integer	123 country_Tanzania Integer	123 country_Uganda Integer	123 country_Zambia Integer	123 country_Zanzibar Integer
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Rows: 1-100 of 53187 | Columns: 50

Let’s create our principal component analysis (PCA) model.

[25]:

from verticapy.learn.decomposition import PCA
vp.drop("africa_pca")
model = PCA(name = "africa_pca")
model.fit("africa_clean",
          africa.get_columns(exclude_columns = ["student_score"]))
africa_pca = model.transform()
display(africa_pca)

	123 student_score Float(22)	123 col1 Float(22)	123 col2 Float(22)	123 col3 Float(22)	123 col4 Float(22)	123 col5 Float(22)	123 col6 Float(22)	123 col7 Float(22)	123 col8 Float(22)	123 col9 Float(22)	123 col10 Float(22)	123 col11 Float(22)	123 col12 Float(22)	123 col13 Float(22)	123 col14 Float(22)	123 col15 Float(22)	123 col16 Float(22)	123 col17 Float(22)	123 col18 Float(22)	123 col19 Float(22)	123 col20 Float(22)	123 col21 Float(22)	123 col22 Float(22)	123 col23 Float(22)	123 col24 Float(22)	...	123 col72 Float(22)	123 col73 Float(22)	123 col74 Float(22)	123 col75 Float(22)	123 col76 Float(22)	123 col77 Float(22)	123 col78 Float(22)	123 col79 Float(22)	123 col80 Float(22)	123 col81 Float(22)	123 col82 Float(22)	123 col83 Float(22)	123 col84 Float(22)	123 col85 Float(22)	123 col86 Float(22)	123 col87 Float(22)	123 col88 Float(22)	123 col89 Float(22)	123 col90 Float(22)	123 col91 Float(22)	123 col92 Float(22)	123 col93 Float(22)	123 col94 Float(22)	123 col95 Float(22)	123 col96 Float(22)
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17	473.825234391116	-32.7424357488911	0.240517591260245	-11.1667414061372	1.65440479313955	-1.2703512490378	-1.43570505297003	0.642798710767198	0.0402684116569747	-0.24147442982037	-0.178509599366519	0.212272541155645	-0.121463353289044	-0.994159542850418	0.658206972757151	-0.250078725621494	0.0284689065751471	1.10596346846344	0.128989458824467	0.470231691109332	0.330674787709554	-0.436119197327841	-0.136388269242003	0.0585892967973059	-0.100384967120591	...	-0.00858573974399424	0.0870251285539719	-0.105975939127315	-0.00361292621400515	-0.029611338339579	-0.00793150267721557	-0.144639813413156	-0.0198622950689913	-0.0870080825374104	-0.0171928031465839	-0.00969898200927332	0.00522990856217091	0.0178902306603745	0.00383529625990871	0.0442538133777875	0.0067883525126471	0.0019255526598696	-0.00537389486310926	-0.00236219429224603	0.00112733962230964	-0.000452583286840586	0.000135198344831308	0.00017539987203731	-6.78492626069434e-05	-8.80226474891461e-05
18	544.095820873929	-32.7310334925601	0.313906263846903	-11.1051208257563	2.62892311271962	-0.999800920799761	-1.18538159900383	0.66223737232509	-0.113443526622243	-0.0635662962382578	-0.788166584361524	-0.15279908486917	-0.215608473855243	-0.558258746943725	0.0386670043385297	-0.0367706054047864	0.0903891833184159	-0.0678793722670745	-0.421370629851709	0.408102486825384	0.687263260357507	-0.219224256872766	-0.118570750108595	-0.0277697857044199	0.289148276037131	...	0.102048049721679	-0.214071379953787	-0.12001676820263	-0.0191654095933551	-0.0039096493508677	-0.115435148160958	-0.102785277089626	0.0102320624009359	-0.0765040578350052	-0.00848229963247724	0.021193669984678	3.30793124233815e-05	0.0316752937969186	0.0025255273287994	0.0451574355650565	0.0137708751554172	0.00218061316159434	0.00804429751154718	-0.000991074992504673	-0.000543291056348593	0.000918159873030154	0.000532632352805884	-0.000499563385623738	-0.000531123528301044	-0.000154706610857041
19	564.874824604798	-32.7401270187197	0.253280805389215	-11.1459385057673	2.08866691037721	-1.03439347182467	0.854091795716144	0.630563755785982	0.319478423241122	0.00889836113356145	-0.129142342032259	0.836067144942318	-0.581198462084677	-0.0454545831885309	-0.0394800570789401	0.0493663750627059	0.217160580474199	-0.0291676933164022	-0.324369102243174	0.272043667407118	0.78080007756625	-0.423062344900625	-0.247770525587408	0.0528609384462003	-0.288512536444729	...	-0.0314136960129452	0.12254848348462	-0.0815725354395562	0.0149862262956522	0.0304505895102444	-0.0308403833779038	-0.15696372600075	-0.0631787200094682	-0.0648579830211445	-0.010812770398994	-0.00956533313146808	0.00818708327387518	0.0390691320603987	-0.00100500437971116	0.0158564783107192	0.0121348495253025	-0.00204968497317178	0.0128367735776422	-0.0014590741504854	0.00218229497597339	0.000403242000956009	0.000360192037216096	-4.67365654440936e-06	-0.00034780443186225	-8.92385425244869e-05
20	386.940445160128	-146.007935274002	2.98361260134309	-1.73643824945895	-2.11879961524432	-2.2507390303356	-0.370808879064786	0.536930958364216	-0.137117548038342	-0.00434005351109457	-0.358768710004055	0.453472424137196	-0.664323696760063	0.204906112858067	0.305355632158038	0.636630407779412	-0.103099469767444	-0.048434763384132	-0.147466193553566	-0.350740614844874	-0.124408070401541	0.21701611081367	0.0747267176225849	0.09063794196624	-0.101309258926348	...	-0.107867108597932	0.11419106876823	0.0140149672471478	0.0654182263638838	0.126388405373804	-0.0753440918629819	-0.0898072274564995	0.0342618476751217	-0.0272992137100299	0.0092258792502634	-0.0235275723194489	0.0277194653558964	-0.386133753609336	-0.0172969042734018	-0.0119441124890765	-0.044624810767606	-0.0152208863890718	-0.0185846178733226	0.0062068681197599	0.000139060102342116	-0.00180445697352597	-9.00603534784825e-05	0.000294581523070204	0.000271414522177143	-8.8766076909562e-05
21	458.501728934408	-99.7531631844625	0.456755135508891	-9.31615530815361	-0.182101250426506	-1.77731092917076	0.0774819822794304	0.358539798499385	-0.420976038288105	-0.0612724794064335	0.563889347341643	0.695651433270047	-0.299815143430578	0.335527999369492	-0.523532436729405	0.173487936235884	0.22337839259822	0.20925988654356	-0.252390335509189	0.231252554218047	-0.223150437318622	0.370568214152833	-0.629745548355328	0.602797968443149	0.0162182567491927	...	0.0178423574354346	0.0632245803485244	-0.0867884936547239	0.0796232061541606	0.101287198836249	-0.0582675806305915	0.011974285109584	0.00205800973502652	-0.0492678970080972	0.0113945656494775	0.00228949294648959	0.00249265735074345	0.0219289182899498	0.00642002543601577	-0.000293699046866422	0.00645731585832362	-0.0137995055882705	0.00084718765913821	0.00837902165324989	0.00182188172811587	-0.00151885197744076	1.77940467861402e-05	-0.000512126929066046	-0.000461002336515922	-2.30789436954852e-06
22	460.360232184133	-145.967827438781	3.24209723897023	-1.51739560516103	1.45629723798883	-1.18750332507978	1.52620059463056	0.668096769061844	-0.092262489396949	0.338903828313131	-0.584441323975356	0.419036453565346	0.407249087982467	-0.32311132706284	0.152730253962708	-0.23498534039991	-0.126384749823476	0.382570696139862	0.626802405832989	0.747215024171856	-0.338158170097106	-0.287956453838254	0.015507220812624	-0.0760230998318135	0.283719626232766	...	-0.0579036296253949	-0.0821329302235731	0.000585339799953926	0.0286232090325094	0.115135709908383	-0.0457586503355612	0.0143204300985935	-0.0151569234254257	-0.00582072192730223	0.0247554548729577	-0.0138992183420362	0.00338528162586345	0.0364552168795634	-0.00122076263247838	-0.0245645023590314	-0.00277931343137256	-0.0214075223938752	-0.0031876406568651	0.0065565189698234	-0.000589087154433834	-0.00109246486259286	5.58049970417651e-05	-0.000155062271006442	-0.000133592806482755	-0.000101259551633043
23	457.035551231015	-99.7183065801375	0.692422293223975	-9.14582165285617	2.47308301928862	-1.17900733005693	-2.41775368563068	0.269244846160055	0.389517094898464	-0.0095029861777654	-0.357936806091288	0.35549155593337	0.0974070937254248	0.398662574536493	-0.244520706320029	-0.244239675075445	-0.319658081497666	-0.30587716100593	0.197053713519762	0.32578130400445	-0.631929625151315	0.640285219088249	-0.810231971682159	-0.560578013605192	0.247970294816896	...	0.018483521629228	0.0619539121301092	-0.0510651953154009	0.0445789636667397	0.0334182737542942	-0.0982112080670998	0.0506074865799649	-0.00051068009933595	-0.137757056423279	-0.00680574898183244	0.0183448471876099	0.00318160008726986	0.0220933936761551	-0.0014699090963652	0.0398101126944097	-0.00428217176218627	-0.014131472242007	-0.000104148462761249	0.00690828710832661	0.000132787177170592	-0.00221343486962622	3.49507174680774e-06	-0.000108031628575324	0.000157066817303482	-1.26324904632776e-05
24	504.282977573042	-99.7078856729631	0.760985100398056	-9.08942743999651	3.41849050447846	-0.908848621119775	-2.18310716226175	0.333161324026099	0.17761770222505	0.36432012735638	-0.565807844946837	0.304358503859534	-0.574819634278905	-0.180507754887021	0.0934103370459952	-0.266006571331322	-0.11221271461608	-0.690542003309152	0.0404888063875205	0.763685303865418	0.0273903021047672	0.0739102401472135	0.153171392541128	-0.113853166084175	0.496703178489549	...	-0.106325065384536	-0.197163011678312	-0.0379363437373575	0.0546636348539375	0.0129465016314034	-0.0767370034870977	-0.155333784185802	-0.000845601855885431	-0.0862531391639161	-0.00838475010444501	0.00859639507876128	0.0111997829008831	0.025210710549724	-0.00408342261209095	0.0209076856617417	0.0104735755496759	-0.0145731072832603	0.00524800753151419	0.00798618625430419	0.000661989631434249	-0.00111972545495861	-9.01639047179753e-06	-0.000281881330808003	-0.000261560237320982	-0.000147162526120649
25	475.872247772718	-145.937469981057	3.43256782185581	-1.35640761649934	4.08489858666607	-0.39826569923974	3.12365123395954	0.664066571283182	-0.193321233215491	0.270202323805329	-0.128342083643257	0.0112395764094501	-0.123748530621251	-0.320027383909188	0.483926820296355	-0.388067729375127	-0.340093039191363	0.758376886192911	0.27395573363588	-0.169045927611831	-0.545996149083166	0.0479239556304956	0.0657099932756605	0.0383095807425184	0.124981312897198	...	-0.00788054700916703	0.0437299873500666	-0.118531693127083	0.0148379088423725	0.176315280883512	0.00798952094177881	-0.181169084178455	-0.0310266174353657	-0.0676701816132578	0.039041185093282	-0.00953454726346865	0.0140825315514693	0.0221819499109349	0.00243426003548558	-0.014476055437759	0.00264821066517712	-0.0269899762211596	-0.00591919498927241	0.00671491203163875	0.00375181432987954	-0.0010991245076335	-7.43352978193281e-05	-0.00014520099555754	-2.12660139644502e-06	-2.92296076829335e-05
26	503.899980617811	-135.075139866865	-14.4516465693281	-7.13429393604446	-1.83898476305812	-2.29563412111468	0.221307590641817	0.739503971025698	-0.375316882155617	0.262114324412281	-0.0373430061050481	0.404675862787618	0.351500463866835	-0.42210371607577	0.112754890752416	0.856357415000825	-0.373571580499463	-0.0950984258234397	0.224989612848882	0.716460115369752	0.142346184521599	0.190122473089587	0.484583619639764	0.00257726713485661	0.361793278302011	...	0.000542481607441543	-0.102496560304925	-0.0543819541580344	0.0492415423231661	0.0621763748192287	0.0604030760197813	-0.0317686664205204	-0.210208200968839	0.145738570713264	0.0287123233421631	-0.0354355408218209	0.0101649297956034	0.0139404037265429	0.00249386048466765	-0.0157928883460642	-0.0278841258535506	-0.0179476490234095	-0.0125732016373325	0.0126985655306868	0.000981094169332077	-0.000447547188798717	0.000115323268129696	-0.000838030229745162	0.000303133335482144	9.16333778212053e-05
27	480.484906064866	-135.06437677072	-14.3830648858418	-7.07792897129153	-0.928205289333998	-2.03677202752876	0.443443320893426	0.699561903055996	-0.404835898918602	0.244890113615523	0.0700666932804966	0.495740244578046	0.479073237545845	-0.386292447711553	-0.373433719788549	0.0882885097312115	-0.305743888744309	-0.0491494968110658	0.173108927301416	0.848082154761865	0.00337637174762836	-0.115770534275771	0.299738456205209	-0.0128878906503756	0.452882777800126	...	-0.0117739669460229	-0.100965958983177	-0.0390121418045609	0.0544234046178601	0.0828848116936178	0.0147139541987915	0.0503298060580388	-0.210762910833807	0.143920366889772	0.0252655002351647	-0.0218854980334272	-0.00568195371971901	0.0217643663506194	0.0102864321012746	-0.00763768800004581	-0.0277607731979834	-0.0193565211842954	-0.00479168835059982	0.00829564769329994	-0.000236082954283619	-0.00124169968377287	-0.000411340217303084	-0.00035413859504128	0.000161376939785488	-8.82111806644711e-05
28	516.744491629541	-32.4688404455722	3.0565789805429	7.50128773215979	-0.74152818903014	-1.61725311359219	-1.61692357306311	0.410039801580044	-0.0193253309259366	-0.812909215059272	0.803015119182587	-0.173814536088915	0.113936941190524	-0.419120156958905	0.139214381128877	0.870627808495661	0.141918290130269	0.0456829716333422	-0.16474982597099	-0.481914114918399	-0.0722663437999867	0.323762564434361	-0.294334286028933	-0.52798543867028	0.486635519540559	...	0.00996183132793756	-0.072926051229734	-0.0106680136157848	0.00569176278868715	-0.0202809714400396	0.0268302819424222	0.0364544239266338	-0.200435820298597	-0.00499355553579148	-0.00508857368663763	0.00638368772013721	-0.00189511707401652	0.0261312027253674	0.000634553369935197	0.007940615972704	-0.0245899355494038	0.00152614295057927	-0.00392179248666178	0.00113726442343894	-0.0010206237110153	0.000146178066821925	-0.000161028335524135	-0.00038406964773703	3.00224038809934e-05	-5.46293305209761e-05
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30	506.128325450387	-32.453730619004	3.15894224747872	7.57013724477688	0.432280397864475	-1.32140459774076	-2.29543993524708	0.1142575486569	-0.14238951400938	0.0800736146070289	0.978852553278917	0.68372628702235	-0.328004017418676	-0.455081962154307	-0.0263946586305973	-0.143086990552251	-0.480728342995146	0.0919296554901126	0.179501655677752	-0.10724062763642	-0.415377070719824	-0.0280806731601442	-0.0262273676896543	-0.192296591802352	0.669649943166715	...	-0.0154754199981787	0.311334601086042	-0.0269158188680901	0.0197515775620206	-0.027171645482827	-0.0608522666149993	-0.188549650013747	-0.120183850038612	-0.0586545784083123	-0.0256983281563778	-0.00238142558723773	0.00542502903411895	0.0381424832077668	-0.000757734146571558	0.0480728995540536	0.0295677231294024	0.000384357901425375	0.0138739772716216	-0.00215446083698898	1.70519678808448e-05	-0.000789999557094122	-0.000152440803632103	-9.47840731874895e-05	-7.81698209217631e-05	-1.27191585912149e-05
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95	584.081078168864	-55.5791726532609	25.8003491348088	-9.75781430031778	5.66803878193494	-0.0294357623487914	0.155346404967503	0.358280129734693	-0.411759027551669	-0.295428577742405	-0.158914334429036	-0.093023563794028	0.20847586058674	-0.343897634096707	-0.619180570132857	0.14932133042426	-0.0791842860446841	-0.256412292155309	-0.355005991317141	-0.859286966497489	-0.0786181502471363	-0.27923217768679	-0.264239880105187	0.0216409175248453	0.337435220618117	...	-0.0864044037339756	0.00356562996481445	0.00834118173680603	0.00611496973776915	-0.0260293137637134	0.06939908475877	-0.0543222253443361	-0.024442312386664	-0.201065025065977	-0.0130115149539422	0.0109156795329508	-0.0173139220607323	0.00743521913527134	-0.0126779921244239	-0.0367282837697497	0.00441540319864831	-0.000783715886320987	0.0247642110348968	-0.00204768471791701	-0.0002535696415748	-0.000263739245611695	-0.000274749500833891	-0.000196693017253878	4.30342753571954e-05	-3.757297107826e-05
96	504.241138890166	-55.575901734583	25.8338192575418	-9.74909108349927	5.85097467489563	-0.0194998945573977	-0.761450692067778	0.097665030373862	0.00929590750375321	0.197448464234695	0.0591363653214932	0.456471421141607	-0.190005206541774	0.0759751523955758	-0.482839049760755	0.00859810548871773	-0.53488110793451	-0.657128875671009	0.120333117609483	-0.409980711560635	-0.0256537781300589	-0.160524266415917	-0.202798691075721	-0.119577470679667	0.407350724081079	...	-0.0467256651658579	-0.0351989814210551	0.00191231521672797	0.0281855492520927	-0.0719203290811156	0.0846027995297793	-0.036124270834668	-0.00148684078407537	-0.324284202913091	-0.0313594259604617	0.0376754639412369	-0.00368556021109794	0.00266702224495177	-0.0241747968594218	-0.0193896874788775	0.00245920411402622	-0.00185097015715829	0.00120381862134916	-0.00249297918688546	0.00146624100204053	-0.000158002961409254	5.39912173636254e-06	-0.000333512994950624	-0.000135932826804084	-6.33476850877843e-05
97	451.694405556509	-100.052746518712	-7.16312614030393	-4.38987689622276	-4.29059796730787	-2.71987057925125	2.00362279112501	0.960168925683712	-0.417436648119099	0.383434794620825	-0.517188829028511	-0.403082137911537	-0.446001325773676	-0.391685367160913	0.180728922068404	-0.326396876258889	-0.332092098015725	-0.258715571458783	-0.323106148836575	-0.247573256981777	-0.125379462373252	-0.0987345131234224	-0.0631116612672849	0.091745149010101	-0.0296749286306622	...	0.0658262487248542	0.254932931688263	-0.302469814068952	-0.14461784627311	0.152147445577438	0.766654679223246	-0.0877197098582378	0.026303156161697	0.0166640878222866	0.0716503356430138	-0.0679997555642156	0.00948270093609517	-0.000513798308015875	0.0164185105627167	0.0102047533804613	-0.00981562709683195	-0.0450770160368151	-0.0242790907561151	0.00705503385904597	0.00300169403243212	-0.00227632301695144	-0.000228589676840726	-0.000480145015284477	-0.000134538515380185	6.03417492095299e-05
98	522.558825103114	-100.034335522356	-7.03232445764347	-4.30952774591202	-3.15816511839394	-2.66562628292813	-2.90120975128118	0.730207138652379	-0.362230515333286	-0.0634861169540975	-0.910790302700194	-0.34741761797977	-0.503520851498569	-0.802208442154076	0.181340746192612	-0.246722305704912	-0.251515001271961	-0.14841843836207	-0.611576019392669	0.359080107917354	0.479605789954239	-0.235299495435214	-0.0364029010522326	0.0895703244860192	0.267352517515781	...	-0.18538773290017	0.160365786894645	-0.0846420614244898	0.0515589144733812	-0.252151839174686	0.735988948546572	-0.0468763732410456	0.0268754299710991	0.0764140969092613	-0.00114326769484739	-0.0891787878193202	0.0113869122455269	0.000991105552738605	-0.00460232626284815	-0.0193101664901832	-0.00106985427649817	-0.0218335535882273	-0.0256503552391838	0.00655267670372882	0.00419957463400608	-0.00300871167259851	-0.000659310558231929	-0.000229466430389385	-0.000165274403114058	8.42146303233909e-05
99	422.842681154036	-100.042387372491	-7.08873187776132	-4.34541254525769	-3.66613844776312	-2.7055903934522	-0.883243491245131	0.471157419094709	-0.583007557091503	0.310378393344512	-0.594839662727608	0.69744913894708	0.112285362576085	1.09045137068516	0.675323118818532	0.581228347681134	-0.0637019737666294	0.14827949293098	0.0586737061892043	-0.20951208888963	0.167135041679561	0.102419029181119	-0.268648553565265	-0.0268326431951432	0.0153196572127541	...	-0.0989017732277482	0.278614899294083	-0.0676564104694151	0.0780522779414132	-0.275703033628806	0.944068853969695	0.146565372689103	0.0405257612990741	0.117005313266945	0.45577466515417	0.793211795236523	-0.0565202030417767	-0.00807022936477493	0.0246957339935196	0.0516135537915526	-0.0117585358229407	-0.0257769403735995	-0.0336373143409781	0.0106463065981505	-5.27566916002853e-05	-0.00331451888405102	-0.00103241584188858	-0.000560162793570933	-2.87784153687497e-05	0.000333264912157455
100	515.308862586361	-38.8836848623655	-4.40240378254429	-6.84918720206923	-4.35651033077961	-2.61013403464307	3.24885288820033	0.944052348309602	-0.627284357023917	0.572829696230636	-0.594631674569455	0.358418486896867	0.706079747150057	0.0144078021408922	-0.213147461923853	-0.359184058122795	0.257191249354628	0.218954141903604	0.31060231783415	-0.319042787380765	0.317949746929666	0.53763578354052	-0.0523222712690421	-0.0428025760183886	-0.0549940873372601	...	-0.139661500021062	0.0502866976130115	0.00871907902777556	0.429629308985378	-0.712357910808636	-0.288156407627618	-0.00569460339001161	-0.0183421158154477	-0.0915965056561863	0.410871739921508	-0.229135833899999	0.0108467153884244	0.00284625405114677	0.028533699148518	-0.0217019493784513	-0.00644535175603426	-0.0688335704010482	-0.00529860784278855	0.00555307361234217	0.00351138990124526	0.00368359976941893	0.000229921711220564	-0.000941145401024069	-0.000101930184223374	0.000488982312495705

Rows: 1-100 | Columns: 50

We can verify the Gauss-Markov assumptions with our PCA model.

[28]:

vp.set_option("plotting_lib","matplotlib")
africa_pca.corr()

[28]:

<AxesSubplot:>

../../../_images/notebooks_full_stack_linear_regression_index_43_1.png

Let’s use a cross-validation to test our linear regression model.

[27]:

cross_validate(LinearRegression("africa_lr", solver = "BFGS"),
               input_relation = africa_pca,
               X = africa_pca.get_columns(exclude_columns = ["student_score"]),
               y = "student_score")

[27]:

	explained_variance	max_error	median_absolute_error	mean_absolute_error	mean_squared_error	root_mean_squared_error	r2	r2_adj	aic	bic	time
1-fold	0.406542147837413	381.377381967434	42.321802457313	52.1549710082439	4509.13724865015	67.1501098186008	0.406506116847415	0.403276584323741	149449.626786821	150202.48387636	4.423546075820923
2-fold	0.410222146579686	382.456645738697	42.5006435686933	51.9942401728598	4445.04112569299	66.6711416258413	0.410222003523684	0.407012145387638	149170.464279923	149923.304598801	4.633985996246338
3-fold	0.405169553262685	386.242511844056	42.04831284786	51.6820005012826	4439.37800301321	66.6286575207186	0.405168924305424	0.401929360949965	149047.075875319	149799.849082548	4.766168117523193
avg	0.40731128255992805	383.35884651672905	42.29025295795543	51.9437372274621	4464.518792452117	66.81663632172024	0.4072990148921743	0.40407269688711467	149222.38898068768	149975.21251923635	4.607900063196818
std	0.0021332058773568005	2.086120300463872	0.186005911079332	0.1963639235945825	31.634608840565697	0.23643837060050404	0.0021377430276719577	0.002150041987207658	168.3922801078864	168.42311490201922	0.14108584335398106

Rows: 1-5 | Columns: 12

As you can see, we’ve created a much more accurate model here than in our first attempt. This example emphasizes the importance of filtering noise from the data.

Conclusion#

We’ve seen two techniques that can help us create powerful linear regression models. While the first method normalized the data and looked for correlations, the second method applied a PCA model. The second one allows us to confirm the Gauss-Markov assumptions - an essential part of using linear models.

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