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verticapy.machine_learning.vertica.ensemble.RandomForestRegressor.regression_report

RandomForestRegressor.regression_report(metrics: str | Literal[None, 'anova', 'details'] | list[Literal['aic', 'bic', 'r2', 'rsquared', 'mae', 'mean_absolute_error', 'mse', 'mean_squared_error', 'msle', 'mean_squared_log_error', 'max', 'max_error', 'median', 'median_absolute_error', 'var', 'explained_variance']] | None = None) → float | TableSample

Computes a regression report using multiple metrics to evaluate the model (r2, mse, max error…).

metrics: str | list, optional

The metrics used to compute the regression report.

• None:

  Computes the model different metrics.

• anova:

  Computes the model ANOVA table.

• details:

  Computes the model details.

It can also be a list of the metrics used to compute the final report.

• aic:

  Akaike’s Information Criterion

  \[AIC = 2k - 2\ln(\hat{L})\]

• bic:

  Bayesian Information Criterion

  \[BIC = -2\ln(\hat{L}) + k \ln(n)\]

• max:

  Max Error.

  \[ME = \max_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• mae:

  Mean Absolute Error.

  \[MAE = \frac{1}{n} \sum_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• median:

  Median Absolute Error.

  \[MedAE = \text{median}_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• mse:

  Mean Squared Error.

  \[MsE = \frac{1}{n} \sum_{i=1}^{n} \left( y_i - \hat{y}_i \right)^2\]

• msle:

  Mean Squared Log Error.

  \[MSLE = \frac{1}{n} \sum_{i=1}^{n} (\log(1 + y_i) - \log(1 + \hat{y}_i))^2\]

• r2:

  R squared coefficient.

  \[R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2}\]

• r2a:

  R2 adjusted

  \[\text{Adjusted } R^2 = 1 - \frac{(1 - R^2)(n - 1)}{n - k - 1}\]

• qe:

  quantile error, the quantile must be included in the name. Example: qe50.1% will return the quantile error using q=0.501.

• rmse:

  Root-mean-squared error

  \[RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}\]

• var:

  Explained Variance

  \[\text{Explained Variance} = 1 - \frac{Var(y - \hat{y})}{Var(y)}\]

TableSample

report.

We import verticapy:

import verticapy as vp

For this example, we will use the winequality dataset.

import verticapy.datasets as vpd

data = vpd.load_winequality()

	123 fixed_acidity Numeric(8)	123 volatile_acidity Numeric(9)	123 citric_acid Numeric(8)	123 residual_sugar Numeric(9)	123 chlorides Float(22)	123 free_sulfur_dioxide Numeric(9)	123 total_sulfur_dioxide Numeric(9)	123 density Float(22)	123 pH Numeric(8)	123 sulphates Numeric(8)	123 alcohol Float(22)	123 quality Integer	123 good Integer	Abc color Varchar(20)
1	3.9	0.225	0.4	4.2	0.03	29.0	118.0	0.989	3.57	0.36	12.8	8	1	white
2	4.7	0.335	0.14	1.3	0.036	69.0	168.0	0.99212	3.47	0.46	10.5	5	0	white
3	4.7	0.455	0.18	1.9	0.036	33.0	106.0	0.98746	3.21	0.83	14.0	7	1	white
4	4.7	0.785	0.0	3.4	0.036	23.0	134.0	0.98981	3.53	0.92	13.8	6	0	white
5	4.9	0.345	0.34	1.0	0.068	32.0	143.0	0.99138	3.24	0.4	10.1	5	0	white
6	4.9	0.345	0.34	1.0	0.068	32.0	143.0	0.99138	3.24	0.4	10.1	5	0	white
7	4.9	0.42	0.0	2.1	0.048	16.0	42.0	0.99154	3.71	0.74	14.0	7	1	red
8	5.0	0.27	0.4	1.2	0.076	42.0	124.0	0.99204	3.32	0.47	10.1	6	0	white
9	5.0	0.31	0.0	6.4	0.046	43.0	166.0	0.994	3.3	0.63	9.9	6	0	white
10	5.0	0.4	0.5	4.3	0.046	29.0	80.0	0.9902	3.49	0.66	13.6	6	0	red
11	5.0	0.44	0.04	18.6	0.039	38.0	128.0	0.9985	3.37	0.57	10.2	6	0	white
12	5.1	0.11	0.32	1.6	0.028	12.0	90.0	0.99008	3.57	0.52	12.2	6	0	white
13	5.1	0.14	0.25	0.7	0.039	15.0	89.0	0.9919	3.22	0.43	9.2	6	0	white
14	5.1	0.165	0.22	5.7	0.047	42.0	146.0	0.9934	3.18	0.55	9.9	6	0	white
15	5.1	0.33	0.22	1.6	0.027	18.0	89.0	0.9893	3.51	0.38	12.5	7	1	white
16	5.1	0.33	0.22	1.6	0.027	18.0	89.0	0.9893	3.51	0.38	12.5	7	1	white
17	5.1	0.33	0.22	1.6	0.027	18.0	89.0	0.9893	3.51	0.38	12.5	7	1	white
18	5.1	0.39	0.21	1.7	0.027	15.0	72.0	0.9894	3.5	0.45	12.5	6	0	white
19	5.2	0.2	0.27	3.2	0.047	16.0	93.0	0.99235	3.44	0.53	10.1	7	1	white
20	5.2	0.21	0.31	1.7	0.048	17.0	61.0	0.98953	3.24	0.37	12.0	7	1	white
21	5.2	0.22	0.46	6.2	0.066	41.0	187.0	0.99362	3.19	0.42	9.73333333333333	5	0	white
22	5.2	0.31	0.2	2.4	0.027	27.0	117.0	0.98886	3.56	0.45	13.0	7	1	white
23	5.2	0.32	0.25	1.8	0.103	13.0	50.0	0.9957	3.38	0.55	9.2	5	0	red
24	5.2	0.34	0.37	6.2	0.031	42.0	133.0	0.99076	3.25	0.41	12.5	6	0	white
25	5.2	0.36	0.02	1.6	0.031	24.0	104.0	0.9896	3.44	0.35	12.2	6	0	white
26	5.2	0.365	0.08	13.5	0.041	37.0	142.0	0.997	3.46	0.39	9.9	6	0	white
27	5.2	0.48	0.04	1.6	0.054	19.0	106.0	0.9927	3.54	0.62	12.2	7	1	red
28	5.2	0.5	0.18	2.0	0.036	23.0	129.0	0.98949	3.36	0.77	13.4	7	1	white
29	5.3	0.16	0.39	1.0	0.028	40.0	101.0	0.99156	3.57	0.59	10.6	6	0	white
30	5.3	0.16	0.39	1.0	0.028	40.0	101.0	0.99156	3.57	0.59	10.6	6	0	white
31	5.3	0.165	0.24	1.1	0.051	25.0	105.0	0.9925	3.32	0.47	9.1	5	0	white
32	5.3	0.23	0.56	0.9	0.041	46.0	141.0	0.99119	3.16	0.62	9.7	5	0	white
33	5.3	0.3	0.3	1.2	0.029	25.0	93.0	0.98742	3.31	0.4	13.6	7	1	white
34	5.3	0.33	0.3	1.2	0.048	25.0	119.0	0.99045	3.32	0.62	11.3	6	0	white
35	5.3	0.36	0.27	6.3	0.028	40.0	132.0	0.99186	3.37	0.4	11.6	6	0	white
36	5.3	0.36	0.27	6.3	0.028	40.0	132.0	0.99186	3.37	0.4	11.6	6	0	white
37	5.3	0.4	0.25	3.9	0.031	45.0	130.0	0.99072	3.31	0.58	11.75	7	1	white
38	5.3	0.47	0.11	2.2	0.048	16.0	89.0	0.99182	3.54	0.88	13.6	7	1	red
39	5.3	0.47	0.11	2.2	0.048	16.0	89.0	0.99182	3.54	0.88	13.5666666666667	7	1	red
40	5.3	0.715	0.19	1.5	0.161	7.0	62.0	0.99395	3.62	0.61	11.0	5	0	red
41	5.4	0.22	0.29	1.2	0.045	69.0	152.0	0.99178	3.76	0.63	11.0	7	1	white
42	5.4	0.595	0.1	2.8	0.042	26.0	80.0	0.9932	3.36	0.38	9.3	5	0	white
43	5.4	0.74	0.09	1.7	0.089	16.0	26.0	0.99402	3.67	0.56	11.6	6	0	red
44	5.5	0.12	0.33	1.0	0.038	23.0	131.0	0.99164	3.25	0.45	9.8	5	0	white
45	5.5	0.12	0.33	1.0	0.038	23.0	131.0	0.99164	3.25	0.45	9.8	5	0	white
46	5.5	0.14	0.27	4.6	0.029	22.0	104.0	0.9949	3.34	0.44	9.0	5	0	white
47	5.5	0.14	0.27	4.6	0.029	22.0	104.0	0.9949	3.34	0.44	9.0	5	0	white
48	5.5	0.16	0.31	1.2	0.026	31.0	68.0	0.9898	3.33	0.44	11.65	6	0	white
49	5.5	0.16	0.31	1.2	0.026	31.0	68.0	0.9898	3.33	0.44	11.6333333333333	6	0	white
50	5.5	0.18	0.22	5.5	0.037	10.0	86.0	0.99156	3.46	0.44	12.2	5	0	white
51	5.5	0.24	0.45	1.7	0.046	22.0	113.0	0.99224	3.22	0.48	10.0	5	0	white
52	5.5	0.29	0.3	1.1	0.022	20.0	110.0	0.98869	3.34	0.38	12.8	7	1	white
53	5.5	0.31	0.29	3.0	0.027	16.0	102.0	0.99067	3.23	0.56	11.2	6	0	white
54	5.5	0.32	0.45	4.9	0.028	25.0	191.0	0.9922	3.51	0.49	11.5	7	1	white
55	5.5	0.35	0.35	1.1	0.045	14.0	167.0	0.992	3.34	0.68	9.9	6	0	white
56	5.5	0.375	0.38	1.7	0.036	17.0	98.0	0.99142	3.29	0.39	10.5	6	0	white
57	5.6	0.15	0.26	5.55	0.051	51.0	139.0	0.99336	3.47	0.5	11.0	6	0	white
58	5.6	0.15	0.31	5.3	0.038	8.0	79.0	0.9923	3.3	0.39	10.5	6	0	white
59	5.6	0.16	0.27	1.4	0.044	53.0	168.0	0.9918	3.28	0.37	10.1	6	0	white
60	5.6	0.175	0.29	0.8	0.043	20.0	67.0	0.99112	3.28	0.48	9.9	6	0	white
61	5.6	0.185	0.19	7.1	0.048	36.0	110.0	0.99438	3.26	0.41	9.5	6	0	white
62	5.6	0.185	0.19	7.1	0.048	36.0	110.0	0.99438	3.26	0.41	9.5	6	0	white
63	5.6	0.22	0.32	1.2	0.024	29.0	97.0	0.98823	3.2	0.46	13.05	7	1	white
64	5.6	0.26	0.18	1.4	0.034	18.0	135.0	0.99174	3.32	0.35	10.2	6	0	white
65	5.6	0.26	0.26	5.7	0.031	12.0	80.0	0.9923	3.25	0.38	10.8	5	0	white
66	5.6	0.26	0.5	11.4	0.029	25.0	93.0	0.99428	3.23	0.49	10.5	6	0	white
67	5.6	0.28	0.28	4.2	0.044	52.0	158.0	0.992	3.35	0.44	10.7	7	1	white
68	5.6	0.3	0.1	6.4	0.043	34.0	142.0	0.99382	3.14	0.48	9.8	5	0	white
69	5.6	0.35	0.14	5.0	0.046	48.0	198.0	0.9937	3.3	0.71	10.3	5	0	white
70	5.6	0.49	0.13	4.5	0.039	17.0	116.0	0.9907	3.42	0.9	13.7	7	1	white
71	5.6	0.49	0.13	4.5	0.039	17.0	116.0	0.9907	3.42	0.9	13.7	7	1	white
72	5.6	0.66	0.0	2.2	0.087	3.0	11.0	0.99378	3.71	0.63	12.8	7	1	red
73	5.6	0.66	0.0	2.2	0.087	3.0	11.0	0.99378	3.71	0.63	12.8	7	1	red
74	5.7	0.15	0.47	11.4	0.035	49.0	128.0	0.99456	3.03	0.34	10.5	8	1	white
75	5.7	0.18	0.26	2.2	0.023	21.0	95.0	0.9893	3.07	0.54	12.3	6	0	white
76	5.7	0.18	0.36	1.2	0.046	9.0	71.0	0.99199	3.7	0.68	10.9	7	1	white
77	5.7	0.2	0.3	2.5	0.046	38.0	125.0	0.99276	3.34	0.5	9.9	6	0	white
78	5.7	0.21	0.32	0.9	0.038	38.0	121.0	0.99074	3.24	0.46	10.6	6	0	white
79	5.7	0.21	0.37	4.5	0.04	58.0	140.0	0.99332	3.29	0.62	10.6	6	0	white
80	5.7	0.22	0.2	16.0	0.044	41.0	113.0	0.99862	3.22	0.46	8.9	6	0	white
81	5.7	0.22	0.2	16.0	0.044	41.0	113.0	0.99862	3.22	0.46	8.9	6	0	white
82	5.7	0.22	0.2	16.0	0.044	41.0	113.0	0.99862	3.22	0.46	8.9	6	0	white
83	5.7	0.22	0.2	16.0	0.044	41.0	113.0	0.99862	3.22	0.46	8.9	6	0	white
84	5.7	0.22	0.2	16.0	0.044	41.0	113.0	0.99862	3.22	0.46	8.9	6	0	white
85	5.7	0.22	0.29	3.5	0.04	27.0	146.0	0.98999	3.17	0.36	12.1	6	0	white
86	5.7	0.23	0.28	9.65	0.025	26.0	121.0	0.9925	3.28	0.38	11.3	6	0	white
87	5.7	0.25	0.26	12.5	0.049	52.5	106.0	0.99691	3.08	0.45	9.4	6	0	white
88	5.7	0.25	0.26	12.5	0.049	52.5	120.0	0.99691	3.08	0.45	9.4	6	0	white
89	5.7	0.25	0.27	11.5	0.04	24.0	120.0	0.99411	3.33	0.31	10.8	6	0	white
90	5.7	0.26	0.24	17.8	0.059	23.0	124.0	0.99773	3.3	0.5	10.1	5	0	white
91	5.7	0.26	0.24	17.8	0.059	23.0	124.0	0.99773	3.3	0.5	10.1	5	0	white
92	5.7	0.26	0.24	17.8	0.059	23.0	124.0	0.99773	3.3	0.5	10.1	5	0	white
93	5.7	0.27	0.32	1.2	0.046	20.0	155.0	0.9934	3.8	0.41	10.2	6	0	white
94	5.7	0.28	0.24	17.5	0.044	60.0	167.0	0.9989	3.31	0.44	9.4	5	0	white
95	5.7	0.32	0.18	1.4	0.029	26.0	104.0	0.9906	3.44	0.37	11.0	6	0	white
96	5.7	0.32	0.38	4.75	0.033	23.0	94.0	0.991	3.42	0.42	11.8	7	1	white
97	5.7	0.36	0.34	4.2	0.026	21.0	77.0	0.9907	3.41	0.45	11.9	6	0	white
98	5.8	0.14	0.15	6.1	0.042	27.0	123.0	0.99362	3.06	0.6	9.9	6	0	white
99	5.8	0.15	0.32	1.2	0.037	14.0	119.0	0.99137	3.19	0.5	10.2	6	0	white
100	5.8	0.17	0.34	1.8	0.045	96.0	170.0	0.99035	3.38	0.9	11.8	8	1	white

Rows: 1-100 | Columns: 14

Divide your dataset into training and testing subsets.

data = vpd.load_winequality()
train, test = data.train_test_split(test_size = 0.2)

Let’s import the model:

from verticapy.machine_learning.vertica import LinearRegression

Then we can create the model:

model = LinearRegression(
    tol = 1e-6,
    max_iter = 100,
    solver = 'newton',
    fit_intercept = True,
)

We can now fit the model:

model.fit(
    train,
    [
        "fixed_acidity",
        "volatile_acidity",
        "citric_acid",
        "residual_sugar",
        "chlorides",
        "density",
    ],
    "quality",
    test,
)



=======
details
=======
   predictor    |coefficient|std_err | t_value |p_value 
----------------+-----------+--------+---------+--------
   Intercept    | 150.78923 | 6.88727|21.89391 | 0.00000
 fixed_acidity  |  0.14582  | 0.01243|11.72695 | 0.00000
volatile_acidity| -0.69261  | 0.08865|-7.81314 | 0.00000
  citric_acid   | -0.08834  | 0.09630|-0.91734 | 0.35901
 residual_sugar |  0.04444  | 0.00389|11.42960 | 0.00000
   chlorides    |  0.11896  | 0.41785| 0.28469 | 0.77589
    density     |-146.78812 | 7.00539|-20.95361| 0.00000


==============
regularization
==============
type| lambda 
----+--------
none| 1.00000


===========
call_string
===========
linear_reg('"public"."_verticapy_tmp_linearregression_v_mldb_6be886b8979811efa8720242ac120002_"', '"public"."_verticapy_tmp_view_v_mldb_6c2d971c979811efa8720242ac120002_"', '"quality"', '"fixed_acidity", "volatile_acidity", "citric_acid", "residual_sugar", "chlorides", "density"'
USING PARAMETERS optimizer='newton', epsilon=1e-06, max_iterations=100, regularization='none', lambda=1, alpha=0.5, fit_intercept=true)

===============
Additional Info
===============
       Name       |Value
------------------+-----
 iteration_count  |  1  
rejected_row_count|  0  
accepted_row_count|5195 

We can get the entire report using:

result = model.report()

	value
explained_variance	0.165012345216713
max_error	3.20473083588462
median_absolute_error	0.497066119123772
mean_absolute_error	0.606136510634613
mean_squared_error	0.617969461493815
root_mean_squared_error	0.786110336717318
r2	0.164941440599503
r2_adj	0.161072443413091
aic	-612.511454140079
bic	-576.472143861379

Rows: 1-10 | Columns: 2

We can easily get the ANOVA table using:

result = model.report(metrics = "anova")

	Df	SS	MS	F	p_value
Regression	6	156.159006039627	26.0265010066045	41.88972950097292	7.088507005435575e-47
Residual	1295	804.596238864947	0.6213098369613491
Total	1301	963.520737327189

Rows: 1-3 | Columns: 6

Important

For this example, a specific model is utilized, and it may not correspond exactly to the model you are working with. To see a comprehensive example specific to your class of interest, please refer to that particular class.