CODEWITHSUNDEEP
pythonrstatisticslinear-regressiondata-science
Arthur Vaz
Arthur Vaz

Reputation: 401

Linear regression in R and Python - Different results at same problem

I am training my data skills in python which I have learned in R. Although, I have a doubt about a simple linear regression

Climate_change Data: [link here]

Python Script

import os
import pandas as pd
import statsmodels.api as sm



train = df[df.Year>=2006]

X = train[['MEI', 'CO2', 'CH4', 'N2O', 'CFC.11', 'CFC.12', 'TSI', 'Aerosols']]
y = train[['Temp']]
model = sm.OLS(y, X).fit()
predictions = model.predict(X)
model.summary()

Python Result

Dep. Variable: Temp R-squared: 0.972

Model: OLS Adj. R-squared: 0.964

Method: Least Squares F-statistic: 123.1

Date: Mon, 01 Oct 2018 Prob (F-statistic):9.54e-20

Time: 14:52:53 Log-Likelihood: 46.898

No. Observations: 36 AIC: -77.80

Df Residuals: 28 BIC: -65.13

Df Model: 8

Covariance Type: nonrobust

MEI 0.0361

CO2 0.0046

CH4 -0.0023

N2O -0.0141

CFC-11 -0.0312

CFC-12 0.0358

TSI -0.0033

Aerosols 69.9680

Omnibus:8.397 Durbin-Watson: 1.484

Prob(Omnibus):0.015
Jarque-Bera (JB):10.511

Skew: -0.546 Prob(JB): 0.00522

Kurtosis: 5.412
Cond. No. 6.35e+06

R Script

train <- climate_change[climate_change$Year>=2006,]
prev <- lm(Temp ~ ., data = train[,3:NCOL(train)])
summary(prev)

R Result

Residuals: Min 1Q Median 3Q Max -0.221684 -0.032846 0.002042 0.037158 0.167887

Coefficients: MEI 0.036056 CO2 0.004817
CH4 -0.002366 N2O -0.013007 CFC-11 -0.033194 CFC-12 0.037775 TSI 0.009100 Aerosols 70.463329 Residual standard error: 0.07594 on 27 degrees of freedom Multiple R-squared: 0.5346, Adjusted R-squared: 0.3967 F-statistic: 3.877 on 8 and 27 DF, p-value: 0.003721

Question

The R-squared has big difference between them, also the coefficients of independent variable has a bit difference. Someone could explain why?

Upvotes: 4

Views: 3126

Answers (2)

coffeinjunky
coffeinjunky

Reputation: 11514

Just to point this out: statsmodel's least squares fit does by default not include a constant. If we remove the constant from R's fit, we get very similar results to the Python implementation, or the other way around, if we add a constant to the statsmodel-fit, we get similar results to R:

Remove the constant in R's lm-call:

summary(lm(Temp ~ . - 1, data = train[,3:NCOL(train)]))

Call:
lm(formula = Temp ~ . - 1, data = train[, 3:NCOL(train)])

Residuals:
      Min        1Q    Median        3Q       Max 
-0.221940 -0.032347  0.002071  0.037048  0.167294 

Coefficients:
          Estimate Std. Error t value Pr(>|t|)  
MEI       0.036076   0.027983   1.289   0.2079  
CO2       0.004640   0.008945   0.519   0.6080  
CH4      -0.002328   0.002132  -1.092   0.2843  
N2O      -0.014115   0.079452  -0.178   0.8603  
`CFC-11` -0.031232   0.096693  -0.323   0.7491  
`CFC-12`  0.035760   0.103574   0.345   0.7325  
TSI      -0.003283   0.036861  -0.089   0.9297  
Aerosols 69.968040  33.093275   2.114   0.0435 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.07457 on 28 degrees of freedom
Multiple R-squared:  0.9724,    Adjusted R-squared:  0.9645 
F-statistic: 123.1 on 8 and 28 DF,  p-value: < 2.2e-16

Let's add a constant to statsmodel's call:

X_with_constant = sm.add_constant(X)

model = sm.OLS(y, X_with_constant).fit()
model.summary()

gives us identical results:

OLS Regression Results
Dep. Variable:  Temp    R-squared:  0.535
Model:  OLS Adj. R-squared: 0.397
Method: Least Squares   F-statistic:    3.877
Date:   Tue, 02 Oct 2018    Prob (F-statistic): 0.00372
Time:   10:14:03    Log-Likelihood: 46.899
No. Observations:   36  AIC:    -75.80
Df Residuals:   27  BIC:    -61.55
Df Model:   8       
Covariance Type:    nonrobust       
coef    std err t   P>|t|   [0.025  0.975]
const   -17.8663    563.008 -0.032  0.975   -1173.064   1137.332
MEI 0.0361  0.029   1.265   0.217   -0.022  0.095
CO2 0.0048  0.011   0.451   0.656   -0.017  0.027
CH4 -0.0024 0.002   -0.950  0.351   -0.007  0.003
N2O -0.0130 0.088   -0.148  0.884   -0.194  0.168
CFC-11  -0.0332 0.116   -0.285  0.777   -0.272  0.205
CFC-12  0.0378  0.123   0.307   0.761   -0.215  0.290
TSI 0.0091  0.392   0.023   0.982   -0.795  0.813
Aerosols    70.4633 37.139  1.897   0.069   -5.739  146.666
Omnibus:    8.316   Durbin-Watson:  1.488
Prob(Omnibus):  0.016   Jarque-Bera (JB):   10.432
Skew:   -0.535  Prob(JB):   0.00543
Kurtosis:   5.410   Cond. No.   1.06e+08

Upvotes: 3

akrun
akrun

Reputation: 887118

As mentioned in the comments, it could be an issue with multicollinearity based on the warnings given. One way to test whether we get the same r-squared is by using another package sklearn and build the model based on the LinearRegression module

from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

regr = LinearRegression()
regr.fit(X, y)
predictions = regr.predict(X)
r2_score(y, predictions)
#0.5345800653144226

But, LinearRegression wouldn't give any summary output. Have to extract the parameters of interest

Upvotes: 1

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