Interaction Terms

Interaction terms are when we use a derived variable from one or more per-existing variables, it can be multiple or division of these variables.

Adding interaction terms might help in improving the prediction accuracy of the model.

The addition of interaction terms needs prior knowledge of the dataset and variables.

import statsmodels.formula.api as sm model4 = sm.ols(formula='Sales ~ Server_Down_time_Sec+Holiday+Special_Discount+Online_Ad_Paid_ref_links+Social_Network_Ref_links+Month+Weekday+DayofMonth+Holiday*Weekday', data=Webpage_Product_Sales) fitted4 = model4.fit() fitted4.summary()

OLS Regression Results

Dep. Variable:

Sales

R-squared:

0.865

Model:

OLS

Adj. R-squared:

0.863

Method:

Least Squares

F-statistic:

473.6

Date:

Wed, 27 Jul 2016

Prob (F-statistic):

2.17e-282

Time:

12:59:08

Log-Likelihood:

-6355.7

No. Observations:

675

AIC:

1.273e+04

Df Residuals:

665

BIC:

1.278e+04

Df Model:

Covariance Type:

nonrobust

coef

std err

P>|t|

[95.0% Conf. Int.]

Intercept

6753.6923

708.791

9.528

0.000

5361.955 8145.430

Server_Down_time_Sec

-140.4922

12.044

-11.665

0.000

-164.141 -116.844

Holiday

2201.8694

1232.336

1.787

0.074

-217.870 4621.608

Special_Discount

4749.0044

344.145

13.799

0.000

4073.262 5424.747

Online_Ad_Paid_ref_links

5.9515

0.250

23.805

0.000

5.461 6.442

Social_Network_Ref_links

7.0657

0.353

19.994

0.000

6.372 7.760

Month

480.3156

35.597

13.493

0.000

410.420 550.212

Weekday

1164.8864

59.143

19.696

0.000

1048.756 1281.017

DayofMonth

47.0967

13.073

3.603

0.000

21.428 72.766

Holiday:Weekday

4294.6865

281.683

15.247

0.000

3741.592 4847.782

Omnibus:

7.552

Durbin-Watson:

0.867

Prob(Omnibus):

0.023

Jarque-Bera (JB):

7.305

Skew:

0.219

Prob(JB):

0.0259

Kurtosis:

2.740

Cond. No.

2.32e+04

Conclusion – Regression

Try adding the polynomial & interaction terms to your regression line. Sometimes they work like a charm.

Adjusted R-squared is a good measure of training/in time sample error. We can’t be sure about the final model performance based on this. We may have to perform cross-validation to get an idea on testing error.

Outliers can influence the regression line, we need to take care of data sensitization before building the regression line.