(IN EXCEL FORMAT) The owner of Original Italian Pizza restaurant chain wants to
ID: 359868 • Letter: #
Question
(IN EXCEL FORMAT) The owner of Original Italian Pizza restaurant chain wants to understand which variable most strongly influences the sales of his specialty deep-dish pizza. He has gathered data on the monthly sales of deep-dish pizzas at his restaurants and observations on other potentially relevant variables for each of several outlets in central Indiana. These data are provided in the file P10_04.xlsx. Estimate a simple linear regres- sion equation between the quantity sold (Y) and each of the following candidates for the best explanatory variable: average price of deep-dish pizzas, monthly advertising expenditures, and disposable income per household in the areas surrounding the outlets. Which variable is most strongly associated with the number of pizzas sold? Explain your choice.
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 $38,000Explanation / Answer
Avg Price
R-square value is very poor
The p-value of the slope is more than 0.05
Significance F is more than 0.05
Therefore, the above relationship is inadequate, statistically insignificant, and the model is feebly explained by the data.
Monthly Adv Exp
R-square value is adequate
The p-values of the slope and intercept are less than 0.05
Significance F is less than 0.05
Therefore, the above relationship is adequate, statistically significant, and the model is well explained by the data.
Disposable Income per Household
R-square value is very poor
The p-values of the slope and intercept are more than 0.05
Significance F is more than 0.05
Therefore, the above relationship is inadequate, statistically insignificant, and the model is feebly explained by the data.
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Considering the three linear regression models, we infer that the Variable 'Quantity Sold' is strongly associated with the 'Monthly Average Advertising Expenditure' only.
SUMMARY OUTPUT Regression Statistics Multiple R 0.350 R Square 0.123 Adjusted R Square 0.055 Standard Error 12800.111 Observations 15 ANOVA df SS MS F Significance F Regression 1 297738993.6 297738993.6 1.8172 0.2007 Residual 13 2129957006 163842846.6 Total 14 2427696000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 117762.55 40210.82 2.93 0.01 30892.37 204632.74 30892.37 204632.74 Avg Price -4713.46 3496.52 -1.35 0.20 -12267.23 2840.31 -12267.23 2840.31Related Questions
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