Partial Regression Plot

import statsmodels.api as sm
import pandas as pd
from patsy import dmatrices
df = sm.datasets.get_rdataset("Guerry", "HistData").data
df.head()
dept Region Department Crime_pers Crime_prop Literacy Donations Infants Suicides MainCity ... Crime_parents Infanticide Donation_clergy Lottery Desertion Instruction Prostitutes Distance Area Pop1831
0 1 E Ain 28870 15890 37 5098 33120 35039 2:Med ... 71 60 69 41 55 46 13 218.372 5762 346.03
1 2 N Aisne 26226 5521 51 8901 14572 12831 2:Med ... 4 82 36 38 82 24 327 65.945 7369 513.00
2 3 C Allier 26747 7925 13 10973 17044 114121 2:Med ... 46 42 76 66 16 85 34 161.927 7340 298.26
3 4 E Basses-Alpes 12935 7289 46 2733 23018 14238 1:Sm ... 70 12 37 80 32 29 2 351.399 6925 155.90
4 5 E Hautes-Alpes 17488 8174 69 6962 23076 16171 1:Sm ... 22 23 64 79 35 7 1 320.280 5549 129.10

5 rows × 23 columns

df.tail()
dept Region Department Crime_pers Crime_prop Literacy Donations Infants Suicides MainCity ... Crime_parents Infanticide Donation_clergy Lottery Desertion Instruction Prostitutes Distance Area Pop1831
81 86 W Vienne 15010 4710 25 8922 35224 21851 2:Med ... 20 1 44 40 38 65 18 170.523 6990 282.73
82 87 C Haute-Vienne 16256 6402 13 13817 19940 33497 2:Med ... 68 6 78 55 11 84 7 198.874 5520 285.13
83 88 E Vosges 18835 9044 62 4040 14978 33029 2:Med ... 58 34 5 14 85 11 43 174.477 5874 397.99
84 89 C Yonne 18006 6516 47 4276 16616 12789 2:Med ... 32 22 35 51 66 27 272 81.797 7427 352.49
85 200 NaN Corse 2199 4589 49 37015 24743 37016 2:Med ... 81 2 84 83 9 25 1 539.213 8680 195.41

5 rows × 23 columns

selective = ['Department', 'Lottery', 'Literacy', 'Wealth', 'Region']
selective
['Department', 'Lottery', 'Literacy', 'Wealth', 'Region']

df = df[selective]
df.head()
Department Lottery Literacy Wealth Region
0 Ain 41 37 73 E
1 Aisne 38 51 22 N
2 Allier 66 13 61 C
3 Basses-Alpes 80 46 76 E
4 Hautes-Alpes 79 69 83 E 
df.tail()
Department Lottery Literacy Wealth Region
81 Vienne 40 25 68 W
82 Haute-Vienne 55 13 67 C
83 Vosges 14 62 82 E
84 Yonne 51 47 30 C
85 Corse 83 49 37 NaN 
# drop na

df = df.dropna()
df.tail()
Department Lottery Literacy Wealth Region
80 Vendee 68 28 56 W
81 Vienne 40 25 68 W
82 Haute-Vienne 55 13 67 C
83 Vosges 14 62 82 E
84 Yonne 51 47 30 C 
y, X = dmatrices('Lottery ~ Literacy + Wealth + Region', data=df, return_type='dataframe')
y.tail()
Lottery
80 68.0
81 40.0
82 55.0
83 14.0
84 51.0 
y.head()
Lottery
0 41.0
1 38.0
2 66.0
3 80.0
4 79.0 
y[:3]
Lottery
0 41.0
1 38.0
2 66.0 
X[:4]
Intercept Region[T.E] Region[T.N] Region[T.S] Region[T.W] Literacy Wealth
0 1.0 1.0 0.0 0.0 0.0 37.0 73.0
1 1.0 0.0 1.0 0.0 0.0 51.0 22.0
2 1.0 0.0 0.0 0.0 0.0 13.0 61.0
3 1.0 1.0 0.0 0.0 0.0 46.0 76.0 
# Model fit and Summary

model = sm.OLS(y, X)
res = model.fit()
print(res.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                Lottery   R-squared:                       0.338
Model:                            OLS   Adj. R-squared:                  0.287
Method:                 Least Squares   F-statistic:                     6.636
Date:                Thu, 25 Apr 2019   Prob (F-statistic):           1.07e-05
Time:                        20:54:07   Log-Likelihood:                -375.30
No. Observations:                  85   AIC:                             764.6
Df Residuals:                      78   BIC:                             781.7
Df Model:                           6                                         
Covariance Type:            nonrobust                                         
===============================================================================
                  coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------
Intercept      38.6517      9.456      4.087      0.000      19.826      57.478
Region[T.E]   -15.4278      9.727     -1.586      0.117     -34.793       3.938
Region[T.N]   -10.0170      9.260     -1.082      0.283     -28.453       8.419
Region[T.S]    -4.5483      7.279     -0.625      0.534     -19.039       9.943
Region[T.W]   -10.0913      7.196     -1.402      0.165     -24.418       4.235
Literacy       -0.1858      0.210     -0.886      0.378      -0.603       0.232
Wealth          0.4515      0.103      4.390      0.000       0.247       0.656
==============================================================================
Omnibus:                        3.049   Durbin-Watson:                   1.785
Prob(Omnibus):                  0.218   Jarque-Bera (JB):                2.694
Skew:                          -0.340   Prob(JB):                        0.260
Kurtosis:                       2.454   Cond. No.                         371.
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

# Check res params

res.params
Intercept      38.651655
Region[T.E]   -15.427785
Region[T.N]   -10.016961
Region[T.S]    -4.548257
Region[T.W]   -10.091276
Literacy       -0.185819
Wealth          0.451475
dtype: float64

# Check rsquared

res.rsquared
0.337950869192882

# Rainbow test

sm.stats.linear_rainbow(res)
(0.8472339976156916, 0.6997965543621643)

# Plot 

sm.graphics.plot_partregress('Lottery', 'Wealth', ['Region' ,'Literacy'], data=df, obs_labels = False)

png