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Determine a regression model for Italian Deep Dish Pizza.

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 attached files.

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

a. 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.
b. which of the variables in this model have regression coefficients that are statistically different from 0 at the 5% significance level?
c. 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.
d. be sure to interpret the standard error and R2 values.

Attachments

Solution Preview

Please see the attached file.

Regression Analysis
R² 0.950
Adjusted R² 0.936 n 15
R 0.975 k 3
Std. Error 3333.092 Dep. Var. Quantity_Sold

ANOVA table
Source SS df MS F p-value
Regression 2,305,491,451.8607 3 768,497,150.6202 69.17 2.00E-07
Residual 122,204,548.1393 11 11,109,504.3763 ...

Solution Summary

With data gathered about sales and operating expenditures, regression analysis techniques are utilized to analyze sales considering several variables.

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