A supermarket chain is interested in exploring the relationship between the sales of its store-brand canned vegetables (Y variable), the amount spent on promotion of the vegetables in local newspapers (X1 variable), and the amount of shelf space allocated to the brand (X2 variable). One of the chain's supermarkets was randomly selected, and over a 20-week period X1 and X2 were varied. Develop the multiple regression model for predicting the sales that explains how advertising expenditures and shelf space influence sales. ( data info attached )

Study the problem "Promotion of Supermarket Vegetables" and download the data from PromotionsData.xlsx. (Available on BB9)

Form the following analysis of the data:

1) Construct the correlation matrix for the variables Sales, AdExp, and ShelfSpc

2) Run a multiple regression model with Sales as the dependent variable and AdExp and ShelfSpc as the independent variables .

3) Run a multiple regression with Sales as the dependent variable and AdExp, SmallShelf, LargeShelf, SmallAdExp, and LargeAdExp as the independent variables .

4) Remove insignificant variables from the model estimated in the previous step (Model 2) and re-run a multiple regression model.

5) Compare the three estimated models and answer question.