For one of its clients, a marketing research firm would like to predict the weekly food expenditures for households. The independent variables of interest are the number of individuals living in a household, the number of teenagers in it, and the total household income. Data for these variables from randomly selected households can be found in the Excel file food expenditures.xlsx.
a. Construct a regression model using all three independent variables.
b. Interpret the meaning of the regression coefficients.
c. Test the significance of the overall regression model using α = 0.05.
d. Predict the average weekly food expenditure for a household with a weekly income of $ 1,200 and five people, one of whom is a teenager.
e. Construct a 95% confidence interval for the average weekly food expenditure for the household described in part d. Interpret the meaning of the interval.
f. Construct a 95% prediction interval for the weekly food expenditure for the household described in part d. Interpret the meaning of the interval.
g. Test the significance of each independent variable using α = 0.05.
h. Construct a 95% confidence interval for the regression coefficients for the teenager variable. Be sure to interpret the meaning of this confidence interval.
i. Construct a regression model using best subsets. Identify the most appropriate regression model for this problem.