Problem: The owner of the original Italian Pizza restaurant chain would like to predict the sales of his specialty, deep dish pizza. He has gathered data on the monthly sales of deep-dish pizza at his restaurant and observations on other potentially relevant variables for each of his 15 outlets in central Pennsylvania. Please see the table below.
Original Italian Pizza, Inc. Sales and Operating Data
| Outlet_Number |
Quantity_Sold |
Average_Price |
Monthly_Advertising_Expenditures |
Disposable_Income_per_Household |
| 1 |
85,300 |
$10.14 |
$64,800 |
$42,100 |
| 2 |
40,500 |
$10.88 |
$42,800 |
$38,300 |
| 3 |
61,800 |
$12.33 |
$58,600 |
$41,000 |
| 4 |
50,800 |
$12.70 |
$46,500 |
$43,300 |
| 5 |
60,600 |
$12.29 |
$50,700 |
$44,000 |
| 6 |
79,400 |
$9.79 |
$60,100 |
$41,200 |
| 7 |
71,400 |
$11.26 |
$55,600 |
$41,700 |
| 8 |
70,700 |
$11.23 |
$57,900 |
$43,600 |
| 9 |
55,600 |
$11.97 |
$52,100 |
$39,900 |
| 10 |
70,900 |
$12.07 |
$60,700 |
$44,800 |
| 11 |
77,200 |
$10.68 |
$64,400 |
$41,800 |
| 12 |
63,200 |
$12.49 |
$55,600 |
$44,200 |
| 13 |
71,100 |
$12.36 |
$60,900 |
$40,100 |
| 14 |
55,500 |
$9.96 |
$47,200 |
$39,100 |
| 15 |
42,100 |
$11.77 |
$46,100 |
$38,000 |
Question 1: Estimate a multiple regression model between the quantity sold (Y) and the following explanatory variables: average price of deep-dish pizzas, monthly advertising expenditure and disposable income per household in the areas.
Question 2: Which of the variables in this model have regression coefficients that are statistically different from 0 at the 5% significance level?
Question 3: Given your findings in part b, which variables, if any, would you choose to remove from the model estimated in part a? explain your decision.
Question 4: Be sure to interpret the standard error and R2 values.