Question

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 regression equation between the quantity sold (Y) and each of the following candidates for the best explanatory variable: average price of deep-dish pizzas (X1), monthly advertising expenditures (X2), and disposable income per household in the areas surrounding the outlets (X3). Round your answers for intercept coefficients to the nearest whole number and slope coefficients to two decimal places, if necessary. If your answer is negative number, enter "minus" sign.

Answer 1

The linear regression model gives mathematical relationship between two variables, the dependent and independent variables. The linear models between the quantity sold and the variables average price, disposable income and monthly advertising are :

• y = - 4713.46x + 117763
• y = 2.94x - 58384
• y = - 1.75x - 32655

To create a linear model using the data given, we use technology such as a excel or a linear regression calculator :

The linear model created using a linear regression calculator between each of the independent variables and quantity sold are :

Average price of deep - dish and Quantity sold :

• Average price of deep - dish pizza(X)
• Quantity sold (Y)

y = - 4713.46x + 117763

Disposable income and Quantity sold :

• Disposable income (X)
• Quantity sold (Y)

y = 2.94x - 58384

Monthly advertising expenditure and Quantity sold :

• Monthly advertising cost (X)
• Quantity sold (Y)

y = - 1.75x - 32655

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