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.

In [46]:

import verticapy as vp
africa = vp.read_csv("data/africa_education.csv")
africa = africa.select(["(zralocp + zmalocp) / 2 AS student_score",
                        "(zraloct + zmaloct) / 2 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	123 teacher_score Float	123 teacher_year_teaching Numeric(7,3)	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(7,3)	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	537.289572911762	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	537.289572911762	10.0	23	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	7.0	Namibia
4	536.690743411639	537.289572911762	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	537.289572911762	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	537.289572911762	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	537.289572911762	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	537.289572911762	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	537.289572911762	10.0	23	SOMETIMES	>2.5-3KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	14	12.0	Namibia
10	535.805274812767	549.40293941491	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	569.993686161283	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	593.122754483926	3.0	23	SOMETIMES	>2-2.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	5.0	Mozambique
23	460.360232184133	569.993686161283	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	593.122754483926	3.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Mozambique
25	504.282977573042	593.122754483926	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	569.993686161283	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	584.886538196464	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	584.886538196464	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	641.876995222798	20.0	25	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
30	394.65259093503	641.876995222798	20.0	25	NEVER	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia
31	506.128325450387	641.876995222798	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	641.876995222798	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	641.876995222798	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	641.876995222798	20.0	25	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	11.0	Namibia
35	359.385615553614	610.956816556605	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	610.956816556605	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	610.956816556605	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	610.956816556605	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	610.956816556605	30.0	16	SOMETIMES	UP TO 0.5KM	WALK			GAS	0	NEVER	I have my own sitting place	17	[null]	Mozambique
40	[null]	641.477648982361	2.0	16	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	17	4.0	Mozambique
41	428.988211440412	656.225505518354	8.0	23	SOMETIMES	>5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	2.0	Namibia
42	532.255684949772	656.225505518354	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	2.0	Namibia
43	392.664714363554	676.11173539576	8.0	20	ALL THE TIME	>3-3.5KM	WALK			CANDLE	0	NEVER	No place/share	13	4.0	Zambia
44	415.95588691273	656.225505518354	8.0	23	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	4.0	Namibia
45	479.525184773189	656.225505518354	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
46	410.328608434232	656.225505518354	8.0	23	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
47	425.993367323877	656.225505518354	8.0	23	SOMETIMES	>3-3.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	4.0	Namibia
48	409.430742983857	656.225505518354	8.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	5.0	Namibia
49	460.605886281468	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	656.225505518354	8.0	23	SOMETIMES	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	18	6.0	Namibia
56	466.248533790025	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	676.11173539576	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Zambia
63	380.388263378723	656.225505518354	8.0	23	SOMETIMES	>5KM	CAR			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	8.0	Namibia
64	421.344721387902	676.11173539576	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	11	8.0	Zambia
65	486.501284763764	638.008383664231	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	638.008383664231	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	638.008383664231	6.0	24	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	9.0	Namibia
68	514.807687171462	638.008383664231	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	683.217366694882	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	638.008383664231	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	683.217366694882	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	634.222848016075	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	634.222848016075	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	617.7225229859	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	645.715848976398	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	645.715848976398	8.0	20	SOMETIMES	>5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	15	3.0	Malawi
77	422.517903579997	645.715848976398	8.0	20	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	12	5.0	Malawi
78	398.31103066659	651.629260258888	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	639.897815295239	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	645.715848976398	6.0	49	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
81	427.462485792718	623.159046261738	8.0	18	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	13	6.0	Zambia
82	600.91272658553	645.715848976398	6.0	49	SOMETIMES	>2-2.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
83	565.065579807459	645.715848976398	6.0	49	SOMETIMES	>5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
84	540.204883338675	645.715848976398	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	645.715848976398	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	645.715848976398	6.0	49	NEVER	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Namibia
87	439.680053114802	645.715848976398	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Malawi
88	353.773643278958	617.7225229859	1.0	13	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Zambia
89	488.376137298698	645.715848976398	6.0	49	SOMETIMES	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Namibia
90	480.908033418792	645.715848976398	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	645.715848976398	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	651.629260258888	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	623.159046261738	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	645.715848976398	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	645.715848976398	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	645.715848976398	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	645.715848976398	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	645.715848976398	8.0	20	NEVER	>3.5-4KM	WALK			ELECTRIC	0	NEVER	No place/share	14	10.0	Malawi
99	459.986311593889	645.715848976398	6.0	49	SOMETIMES	>2.5-3KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	11.0	Namibia
100	594.667991916549	645.715848976398	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.

In [2]:

africa.count_percent()

Out[2]:

	count	percent
"number_students_school"	60890.0	100.0
"english_at_home"	60890.0	100.0
"travel_distance"	60890.0	100.0
"means_of_travel"	60890.0	100.0
"m_education"	60890.0	100.0
"source_of_lighting"	60890.0	100.0
"days_absent"	60890.0	100.0
"repeated_grades"	60890.0	100.0
"sitting_place"	60890.0	100.0
"age"	60890.0	100.0
"country"	60890.0	100.0
"socio_eco_statut"	60832.0	99.905
"student_score"	60809.0	99.867
"teacher_year_teaching"	60708.0	99.701
"f_education"	60599.0	99.522
"teacher_score"	52122.0	85.6

Rows: 1-16 | Columns: 3

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

In [47]:

africa.dropna()

8988 elements were filtered.

Out[47]:

	123 student_score Float	123 teacher_score Float	123 teacher_year_teaching Numeric(7,3)	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(7,3)	Abc country Varchar(24)
1	425.993367323877	537.289572911762	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	537.289572911762	10.0	23	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	13	7.0	Namibia
3	536.690743411639	537.289572911762	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	537.289572911762	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	537.289572911762	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	537.289572911762	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	537.289572911762	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	537.289572911762	10.0	23	SOMETIMES	>2.5-3KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	14	12.0	Namibia
9	535.805274812767	549.40293941491	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	624.124902231691	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	569.993686161283	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	593.122754483926	3.0	23	SOMETIMES	>2-2.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	5.0	Mozambique
22	460.360232184133	569.993686161283	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	593.122754483926	3.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	7.0	Mozambique
24	504.282977573042	593.122754483926	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	569.993686161283	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	584.886538196464	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	584.886538196464	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	641.876995222798	20.0	25	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
29	394.65259093503	641.876995222798	20.0	25	NEVER	>5KM	WALK			PARAFFIN/OIL	0	NEVER	I have my own sitting place	12	6.0	Namibia
30	506.128325450387	641.876995222798	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	641.876995222798	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	641.876995222798	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	641.876995222798	20.0	25	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	11	11.0	Namibia
34	428.988211440412	656.225505518354	8.0	23	SOMETIMES	>5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	2.0	Namibia
35	532.255684949772	656.225505518354	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	14	2.0	Namibia
36	392.664714363554	676.11173539576	8.0	20	ALL THE TIME	>3-3.5KM	WALK			CANDLE	0	NEVER	No place/share	13	4.0	Zambia
37	415.95588691273	656.225505518354	8.0	23	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	4.0	Namibia
38	479.525184773189	656.225505518354	8.0	23	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
39	410.328608434232	656.225505518354	8.0	23	SOMETIMES	>1-1.5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	4.0	Namibia
40	425.993367323877	656.225505518354	8.0	23	SOMETIMES	>3-3.5KM	WALK			FIRE	0	NEVER	I have my own sitting place	12	4.0	Namibia
41	409.430742983857	656.225505518354	8.0	23	SOMETIMES	>1.5-2KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	5.0	Namibia
42	460.605886281468	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	656.225505518354	8.0	23	SOMETIMES	>2.5-3KM	WALK			CANDLE	0	NEVER	I have my own sitting place	18	6.0	Namibia
49	466.248533790025	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	638.008383664231	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	676.11173539576	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Zambia
56	380.388263378723	656.225505518354	8.0	23	SOMETIMES	>5KM	CAR			PARAFFIN/OIL	0	NEVER	I have my own sitting place	13	8.0	Namibia
57	421.344721387902	676.11173539576	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	11	8.0	Zambia
58	486.501284763764	638.008383664231	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	638.008383664231	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	638.008383664231	6.0	24	SOMETIMES	>0.5-1KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	9.0	Namibia
61	514.807687171462	638.008383664231	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	683.217366694882	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	638.008383664231	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	683.217366694882	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	634.222848016075	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	634.222848016075	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	617.7225229859	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	645.715848976398	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	645.715848976398	8.0	20	SOMETIMES	>5KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	15	3.0	Malawi
70	422.517903579997	645.715848976398	8.0	20	NEVER	>0.5-1KM	WALK			PARAFFIN/OIL	0	NEVER	No place/share	12	5.0	Malawi
71	398.31103066659	651.629260258888	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	639.897815295239	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	645.715848976398	6.0	49	SOMETIMES	>5KM	WALK			CANDLE	0	NEVER	I have my own sitting place	12	6.0	Namibia
74	427.462485792718	623.159046261738	8.0	18	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	13	6.0	Zambia
75	600.91272658553	645.715848976398	6.0	49	SOMETIMES	>2-2.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
76	565.065579807459	645.715848976398	6.0	49	SOMETIMES	>5KM	CAR			ELECTRIC	0	NEVER	I have my own sitting place	12	7.0	Namibia
77	540.204883338675	645.715848976398	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	645.715848976398	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	645.715848976398	6.0	49	NEVER	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Namibia
80	439.680053114802	645.715848976398	8.0	20	SOMETIMES	UP TO 0.5KM	WALK			CANDLE	0	NEVER	No place/share	11	7.0	Malawi
81	353.773643278958	617.7225229859	1.0	13	SOMETIMES	>0.5-1KM	WALK			CANDLE	0	NEVER	I have my own sitting place	13	7.0	Zambia
82	488.376137298698	645.715848976398	6.0	49	SOMETIMES	>1-1.5KM	WALK			ELECTRIC	0	NEVER	I have my own sitting place	11	8.0	Namibia
83	480.908033418792	645.715848976398	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	645.715848976398	6.0	49	SOMETIMES	UP TO 0.5KM	WALK