The retailer "bought" a set of adwords from Google and monitored the performance of those adwords over this time period.

We have daily data on the following variables,

- Whether any sale can be attributable to the adword (SALE [Yes=1 or No=0])

- Number of Clicks (CLICKS) generated by the adword

- Number of impressions (IMPS) adword gets

- The average position (AvgPOS) occupied by the adword.

Higher the AvgPOS, lower is the adword displayed in the rankings and hence less likely to be viewed.

(a) Estimate an appropriate regression model with SALE as your dependent variable and CLICKS, IMPS and AvgPOS as the independent variables.

Report and interpret the estimated coefficient on AvgPOS

(b) Notice that the CLICKS have a 'positive' impact on the likelihood of SALE, while AvgPOS has a 'negative' impact on the likelihood of sale.

Suppose the average position occupied by an adword drops by 3 (i.e. the variable AvgPOS increases by 3). How much should the number of CLICKS increase so that the odds of getting a SALE do not change.

Briefly show your working in support of your answer.

c) We will now investigate the interaction between AvgPOS and CLICKS. Please introduce such an interaction variable in your model and estimate the model.

Report and interpret the estimated coefficient on this interaction variable.

(d) Please use the estimated model (with interaction effects) from part(c) for this question.. An adword currently occupies an average position equal to 1.9 and the number of CLICKS generated by the adword are 5 Suppose the average position occupied by the adword increases by 3 (i.e. the variable AvgPOS drops from 1.9 to 4.9).

By what % do the odds of getting a SALE change?

Please briefly show your calculations.