How many extensions are needed?

Building Response Models in R

Kathrin Gruber

Assistant Professor of Econometrics Erasmus University Rotterdam

summary(extended.model)

Coefficients:
                Estimate Std. Error t value  Pr(>|t|)    
(Intercept)       2.2561     0.5654   3.991  0.000117 ***
PRICE            -2.6857     0.7921  -3.390  0.000959 ***
Price.lag         3.9920     0.7959   5.016  1.96e-06 ***
DISPLAY           0.4570     0.1279   3.572  0.000521 ***
Display.lag       0.5097     0.1180   4.319  3.36e-05 ***
COUPON            1.7531     0.1576  11.121   < 2e-16 ***
Coupon.lag       -0.2098     0.1567  -1.339  0.183344    
DISPLAYCOUPON     2.0087     0.2017   9.960   < 2e-16 ***
DisplayCoupon.lag 0.4489     0.2112   2.126  0.035695 *  

Residual standard error: 0.5 on 114 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.7135,    Adjusted R-squared:  0.6934 
F-statistic:  35.5 on 8 and 114 DF,  p-value: < 2.2e-16

summary(extended.model)

Coefficients:
                Estimate Std. Error t value  Pr(>|t|)    
(Intercept)       2.2561     0.5654   3.991  0.000117 ***
PRICE            -2.6857     0.7921  -3.390  0.000959 ***
Price.lag         3.9920     0.7959   5.016  1.96e-06 ***
DISPLAY           0.4570     0.1279   3.572  0.000521 ***
Display.lag       0.5097     0.1180   4.319  3.36e-05 ***
COUPON            1.7531     0.1576  11.121   < 2e-16 ***
Coupon.lag       -0.2098     0.1567  -1.339  0.183344    
DISPLAYCOUPON     2.0087     0.2017   9.960   < 2e-16 ***
DisplayCoupon.lag 0.4489     0.2112   2.126  0.035695 *  

Residual standard error: 0.5 on 114 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.7135,    Adjusted R-squared:  0.6934 
F-statistic:  35.5 on 8 and 114 DF,  p-value: < 2.2e-16

Dropping predictors

AIC(extended.model)

189.21

AIC(lm(update(extended.model, . ~ . - Coupon.lag), data = sales.data))

189.1284

library(MASS)
final.model <- stepAIC(extended.model, direction = "backward", trace = FALSE)
summary(final.model)

Coefficients:
                 Estimate Std. Error t value  Pr(>|t|)    
(Intercept)        2.1887     0.5651   3.873  0.000179 ***
PRICE             -2.6888     0.7949  -3.383  0.000982 ***
Price.lag          4.0267     0.7982   5.045  1.71e-06 ***
DISPLAY            0.4524     0.1283   3.525  0.000609 ***
Display.lag        0.5447     0.1155   4.717  6.78e-06 ***
COUPON             1.7635     0.1580  11.161   < 2e-16 ***
DISPLAYCOUPON      1.9954     0.2021   9.872   < 2e-16 ***
DisplayCoupon.lag  0.4839     0.2103   2.301  0.023182 *  

Residual standard error: 0.5017 on 115 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.709,    Adjusted R-squared:  0.6913 
F-statistic: 40.04 on 7 and 115 DF,  p-value: < 2.2e-16

Let's practice!

Building Response Models in R