1 Read.me

This is the R file of Case I - Timeless. In this file, we will first overview the data, and then run regressions for cannibalization effects.

2 Data Description

First, please download and load data Timeless.Rdata from Canvas. The data include the following variables:

  • Time: A continuous variable of time (measured by weeks since 2011-01-01)
  • Year: A categorical variable of the year (2011 to 2014)
  • Month: A categorical variable of months of the year (1 to 12)
  • Week: A categorical variable of weeks of the year (1 to 52/53)
  • Simplicity: Weekly sales of Simplicity Style
  • Classic: Weekly sales of Classic Style (0 means not yet introduced and thus no sales)
  • Hipster: Weekly sales of Hipster Style (0 means not yet introduced and thus no sales)
load("Timeless.Rdata")
head(timeless)
##   Time Year Month Week Simplicity Classic Hipster
## 1    1 2011     1    1       3091       0       0
## 2    2 2011     1    2       3449       0       0
## 3    3 2011     1    3       3370       0       0
## 4    4 2011     1    4       3479       0       0
## 5    5 2011     1    5       3569       0       0
## 6    6 2011     2    6       3557       0       0

Next, letโ€™s get an overview of the sales of Simplicity before and after the introduction of the Classic.

library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.0.5
ggplot(timeless, aes(x = Time, y = Simplicity)) +
  geom_line() +
  geom_vline(xintercept = 100, color = "red", linetype = "dashed") + 
  geom_text(aes(x = 100, y = 1000, 
                label = "the introduction of Classic"),color = "red")

3 Regression Analysis

We first run a simple with the sales of Simplicity as DV and the sales of Class as IV.

mdl_1 <- lm(Simplicity ~ 1 + Classic, data = timeless)
summary(mdl_1)
## 
## Call:
## lm(formula = Simplicity ~ 1 + Classic, data = timeless)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2245.5 -1338.2  -522.2   697.2  5628.8 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.166e+03  1.736e+02  23.995  < 2e-16 ***
## Classic     3.421e-01  4.067e-02   8.413 1.27e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1832 on 178 degrees of freedom
## Multiple R-squared:  0.2845, Adjusted R-squared:  0.2805 
## F-statistic: 70.78 on 1 and 178 DF,  p-value: 1.268e-14

Then, we control for the week-of-the-year effects by adding Week as an IV.

mdl_2 <- lm(Simplicity ~ 1 + Classic + Week, data = timeless)
summary(mdl_2)
## 
## Call:
## lm(formula = Simplicity ~ 1 + Classic + Week, data = timeless)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -901.10 -252.44   -4.26  194.68 1159.05 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3181.82594  230.88917  13.781  < 2e-16 ***
## Classic        0.23432    0.01056  22.185  < 2e-16 ***
## Week2        369.79073  325.05410   1.138 0.257434    
## Week3        246.37062  325.05019   0.758 0.449898    
## Week4        302.56231  325.05835   0.931 0.353740    
## Week5        339.76968  325.06864   1.045 0.297920    
## Week6        274.08566  325.06751   0.843 0.400734    
## Week7        152.80579  325.06127   0.470 0.639108    
## Week8        208.53950  325.06941   0.642 0.522348    
## Week9        327.91196  325.08517   1.009 0.315054    
## Week10       422.51371  325.09958   1.300 0.196096    
## Week11       685.31720  325.14527   2.108 0.037036 *  
## Week12        26.01676  325.05310   0.080 0.936334    
## Week13      -155.53645  325.04337  -0.479 0.633117    
## Week14        40.82799  325.05847   0.126 0.900247    
## Week15      -261.35094  325.04126  -0.804 0.422880    
## Week16      -268.96545  325.04421  -0.827 0.409533    
## Week17       205.58797  325.09974   0.632 0.528282    
## Week18       683.75441  325.20906   2.103 0.037499 *  
## Week19      1201.25576  325.36365   3.692 0.000330 ***
## Week20      1372.52259  325.40899   4.218 4.67e-05 ***
## Week21      1758.71897  325.53515   5.403 3.16e-07 ***
## Week22      2309.83158  325.75483   7.091 8.47e-11 ***
## Week23      2756.05194  351.23577   7.847 1.58e-12 ***
## Week24      2903.64168  351.24265   8.267 1.64e-13 ***
## Week25      3204.17775  351.27190   9.122 1.49e-15 ***
## Week26      3809.88179  351.39080  10.842  < 2e-16 ***
## Week27      5799.69923  351.94763  16.479  < 2e-16 ***
## Week28      6717.27349  352.19054  19.073  < 2e-16 ***
## Week29      5864.44763  351.79358  16.670  < 2e-16 ***
## Week30      4874.55470  351.48981  13.868  < 2e-16 ***
## Week31      3088.61652  351.16816   8.795 9.09e-15 ***
## Week32      1391.37696  351.08213   3.963 0.000123 ***
## Week33      -303.53878  351.19372  -0.864 0.389062    
## Week34      -192.34944  351.18496  -0.548 0.584856    
## Week35        27.12943  351.16327   0.077 0.938543    
## Week36       154.18346  351.15536   0.439 0.661359    
## Week37       108.58820  351.16144   0.309 0.757660    
## Week38       236.73138  351.15127   0.674 0.501446    
## Week39       278.43000  351.14860   0.793 0.429320    
## Week40       569.53055  351.12534   1.622 0.107300    
## Week41       884.45950  351.10625   2.519 0.013018 *  
## Week42      1032.85356  351.09887   2.942 0.003885 ** 
## Week43      1714.52131  351.08058   4.884 3.10e-06 ***
## Week44      1952.27197  351.08107   5.561 1.53e-07 ***
## Week45      3099.79410  351.13079   8.828 7.58e-15 ***
## Week46      4788.80450  351.35658  13.629  < 2e-16 ***
## Week47      6156.93192  352.06891  17.488  < 2e-16 ***
## Week48      2389.58058  351.76387   6.793 3.89e-10 ***
## Week49      -523.03883  351.08164  -1.490 0.138778    
## Week50      -735.63997  351.08833  -2.095 0.038145 *  
## Week51      -576.12879  351.08042  -1.641 0.103288    
## Week52       771.17974  351.25209   2.196 0.029958 *  
## Week53       328.99769  398.09241   0.826 0.410119    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 459.7 on 126 degrees of freedom
## Multiple R-squared:  0.9681, Adjusted R-squared:  0.9547 
## F-statistic: 72.18 on 53 and 126 DF,  p-value: < 2.2e-16
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