Q1a.

Summarize the mean vale of revenue for each group of search_stays_on and for each date.

Q1a <- paidsearch %>% 
  group_by(search_stays_on, date) %>% 
  summarise(revenue = mean(revenue))

Q1b

Calculate the log difference between mean revenues in each group of search_stays_on. (This is the log of the average revenue in group of search_stays_on == 1 minus the log of the average revenue in group of search_stays_on == 0.)

• For example, consider the following two observations:

# date        the daily mean vale of `revenue`   search_stays_on
# 1-Apr-12    93650.68                           0
# 1-Apr-12    120277.57                          1

• The log difference of daily mean revenues between the two group of search_stays_on for date 1-Apr-12 is log(120277.57) - log(93650.68).

Q1b <- paidsearch %>% 
  mutate(date = dmy(date)) %>% 
  arrange(dma, date)


paidsearch_sum <- Q1b %>%   
  group_by(search_stays_on, date) %>% 
  summarise(revenue = mean(revenue)) 


paidsearch_sum2 <- paidsearch_sum %>% 
  arrange(date, search_stays_on) %>% 
  pivot_wider(names_from = "search_stays_on", 
              values_from = "revenue") %>% 
  rename(rev_control = `0`,
         rev_treat = `1`) %>% 
  mutate(diff_log = log(rev_control) - log(rev_treat))

Q1c

• Describe the daily trend of the log of the daily mean revenue for each group of search_stays_on before and after May 22, 2012 in one plot using lubridate and ggplot2.

• Describe the daily trend of the log difference of daily mean revenues between the two group of search_stays_on before and after May 22, 2012 using lubridate and ggplot2.

• Make a simple comment on your ggplot results.

ggplot(data = paidsearch_sum2) +
  geom_line(aes(x = date, y = diff_log)) +
  geom_vline(aes(xintercept=ymd("2012-May-22")), 
             color = "black", lty  = 2)

ggplot(data = paidsearch_sum2) +
  geom_line(aes(x = date, y = rev_control), color = 'red') +
  geom_line(aes(x = date, y = rev_treat)) +
  geom_vline(aes(xintercept=ymd("2012-May-22")), 
             color = "black", lty  = 2)

ggplot() +
  geom_line(data = filter(paidsearch_sum, search_stays_on == 0)  ,
            aes(x = date, y = log(revenue)), color = 'blue')+
  geom_line(data = filter(paidsearch_sum, search_stays_on == 1)  ,
            aes(x = date, y = log(revenue)), color = 'red')+
  geom_vline(aes(xintercept=ymd("2012-May-22")), 
             color = "black", lty  = 2)+
  geom_smooth(data = filter(paidsearch_sum, 
                            date <= ymd("2012-May-22")),
              aes(x = date, y = log(revenue)),
              method = lm, lty = 4, se = F) +
  geom_smooth(data = filter(paidsearch_sum, 
                            date >= ymd("2012-May-22")),
              aes(x = date, y = log(revenue)), 
              color = "red",
              method = lm, lty = 4, se = F) +
  geom_smooth(data = filter(paidsearch_sum, 
                            date <= ymd("2012-May-22")),
              aes(x = date, y = log(revenue))) +
  geom_smooth(data = filter(paidsearch_sum, 
                            date >= ymd("2012-May-22")),
              aes(x = date, y = log(revenue)), 
              color = "red") 

• There might not be a significant effect of turning off search engine marketing on eBay’s sales revenue.

For the rest of questions in Question 1, use the following data.frame:

paid_search <- read_csv(
  'https://bcdanl.github.io/data/paid_search.csv')

paid_search$DM <- as.factor(paid_search$DM)
paid_search <- arrange(paid_search, DM, no_paid_search)

• For the questions here, do not divide the data.frame, paid_search, into training and testing data sets.

• Variable description
• DM: an identification number of a designated market i (e.g., Boston, Los Angeles)
• May22_2012: 0 denotes before May 22 and May22_2012 = 1 after.
• no_paid_search: 1 if the paid-search goes off in DM, no_paid_search = 0 otherwise.
• log_revenue: the log of eBay’s sales revenue for DM i and time t

Q1d

Consider the following linear regression model.

dm_reg1 <- lm(log_revenue ~  no_paid_search * May22_2012, 
             data = paid_search )

• Report the regression result.

summary(dm_reg1) 

## 
## Call:
## lm(formula = log_revenue ~ no_paid_search * May22_2012, data = paid_search)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8518 -0.7061 -0.0447  0.7696  3.6521 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               10.948646   0.100495 108.948   <2e-16 ***
## no_paid_search             0.014081   0.176603   0.080    0.936    
## May22_2012                -0.039400   0.142121  -0.277    0.782    
## no_paid_search:May22_2012 -0.006587   0.249754  -0.026    0.979    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.198 on 416 degrees of freedom
## Multiple R-squared:  0.0003231,  Adjusted R-squared:  -0.006886 
## F-statistic: 0.04482 on 3 and 416 DF,  p-value: 0.9874

Q1e

Describe the model in Q1d in words.

Q1f

On average, are the predictions correct in the model in Q1d? Are there systematic errors?

Q1g

Describe the following model in words.

formula <- log_revenue ~  no_paid_search * May22_2012 + DM

Q1h

Estimate the following linear regression model.

dm_reg2 <- lm(log_revenue ~  no_paid_search * May22_2012 + DM, 
              data = paid_search )
stargazer::stargazer(dm_reg1, dm_reg2, 
                     type = 'html', 
                     omit = c("DM"))

• Interpret the beta estimates for the following variables:

  • no_paid_search

  • May22_2012

  • no_paid_search:May22_2012

Q1i

On average, are the predictions correct in the model in Q1h? Are there systematic errors?

Q1j

What would happen to sales revenue if eBay stopped paying for search advertising? Would eBay’s search advertising worth the cost?