Car Seats

Shikhar Kohli (PGP32117)
6th Nov, 2017

Setup

setwd('~/code/DAM')
store.df <- read.csv('datasets/CarSeatsDataV5.csv')
attach(store.df)

MODEL 0: Regress Profit on Advertising and interpret the results

fit1 <- lm(Profit ~ Advertising)
summary(fit1)


Call:
lm(formula = Profit ~ Advertising)

Residuals:
    Min      1Q  Median      3Q     Max 
-171.85  -34.38   -3.78   35.97  168.85 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 147.3290     4.0320  36.540  < 2e-16 ***
Advertising   3.0660     0.4295   7.139 4.49e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 57.05 on 398 degrees of freedom
Multiple R-squared:  0.1135,    Adjusted R-squared:  0.1113 
F-statistic: 50.97 on 1 and 398 DF,  p-value: 4.493e-12

MODEL 1: Regress Profit on Shelf Location and interpret the results

fit2 <- lm(Profit ~ ShelveLoc, data = store.df)
summary(fit2)


Call:
lm(formula = Profit ~ ShelveLoc, data = store.df)

Residuals:
     Min       1Q   Median       3Q      Max 
-163.350  -33.330   -1.365   31.033  153.050 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        120.041      4.808   24.97  < 2e-16 ***
ShelveLoc1-Medium   43.309      5.767    7.51 3.93e-13 ***
ShelveLoc2-Good    112.558      7.016   16.04  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 47.11 on 397 degrees of freedom
Multiple R-squared:  0.3971,    Adjusted R-squared:  0.394 
F-statistic: 130.7 on 2 and 397 DF,  p-value: < 2.2e-16

plot(Profit, ShelveLoc)

plot of chunk unnamed-chunk-3

MODEL 2: Regress Profit on Shelf Location and Advertising and interpret the results

fit3 <- lm(Profit ~ ShelveLoc + Advertising, data = store.df)
summary(fit3)


Call:
lm(formula = Profit ~ ShelveLoc + Advertising, data = store.df)

Residuals:
     Min       1Q   Median       3Q      Max 
-145.446  -25.160    0.039   24.796  104.054 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        103.014      4.886  21.085  < 2e-16 ***
ShelveLoc1-Medium   42.433      5.325   7.968 1.73e-14 ***
ShelveLoc2-Good    109.453      6.489  16.867  < 2e-16 ***
Advertising          2.738      0.328   8.347 1.18e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 43.5 on 396 degrees of freedom
Multiple R-squared:  0.4873,    Adjusted R-squared:  0.4834 
F-statistic: 125.4 on 3 and 396 DF,  p-value: < 2.2e-16

MODEL 3: Regress Profit on Shelf Location and Advertising and interpret the results

fit4 <- lm(Profit ~ ShelveLoc * Advertising, data = store.df)
summary(fit4)


Call:
lm(formula = Profit ~ ShelveLoc * Advertising, data = store.df)

Residuals:
     Min       1Q   Median       3Q      Max 
-143.299  -24.554    1.032   24.480  106.201 

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                   108.6051     6.1743  17.590  < 2e-16 ***
ShelveLoc1-Medium              34.6937     7.4206   4.675 4.04e-06 ***
ShelveLoc2-Good               103.1563     9.3093  11.081  < 2e-16 ***
Advertising                     1.8390     0.6903   2.664  0.00803 ** 
ShelveLoc1-Medium:Advertising   1.2276     0.8190   1.499  0.13472    
ShelveLoc2-Good:Advertising     0.9950     0.9812   1.014  0.31118    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 43.48 on 394 degrees of freedom
Multiple R-squared:  0.4902,    Adjusted R-squared:  0.4837 
F-statistic: 75.77 on 5 and 394 DF,  p-value: < 2.2e-16

MODEL 4: Regress Profit on {Advertising, Shelf Location, Competitor's Price, Population, Income, Age, Education, Urban/Rural, US/Outside US}. Interpret the results. Compare MODEL 4 with MODEL 2.

fit5 <- lm(Profit ~ Advertising + ShelveLoc + CompPrice + Population + Income + Age + Education + Urban + US, data = store.df)
summary(fit5)


Call:
lm(formula = Profit ~ Advertising + ShelveLoc + CompPrice + Population + 
    Income + Age + Education + Urban + US, data = store.df)

Residuals:
     Min       1Q   Median       3Q      Max 
-159.654  -17.856    2.075   20.401   68.740 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)       -60.136334  18.171281  -3.309  0.00102 ** 
Advertising         2.959638   0.334864   8.838  < 2e-16 ***
ShelveLoc1-Medium  44.625673   3.797403  11.752  < 2e-16 ***
ShelveLoc2-Good   109.212841   4.608355  23.699  < 2e-16 ***
CompPrice           1.563453   0.101946  15.336  < 2e-16 ***
Population          0.005803   0.011149   0.521  0.60299    
Income              0.370657   0.055560   6.671 8.73e-11 ***
Age                -0.952238   0.095685  -9.952  < 2e-16 ***
Education          -0.679343   0.593883  -1.144  0.25337    
UrbanYes            2.981043   3.402003   0.876  0.38143    
USYes              -5.783463   4.511614  -1.282  0.20064    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 30.69 on 389 degrees of freedom
Multiple R-squared:  0.7493,    Adjusted R-squared:  0.7429 
F-statistic: 116.3 on 10 and 389 DF,  p-value: < 2.2e-16