Chapter 14, Problem 45PS

Zagat’s publishes restaurant rating for various locations in the United States. The file Restaurants contains the Zagat rating for food, décor, service and cost per person for a sample of 50 center city restaurants and 50 metro area restaurants.

Develop a regression model to predict the cost per person, based on a variable that represents the sum of the rating for food, décor, and service ad a dummy variable concerning location (center city versus metro area). For (a) through (m), do not include an interaction term.

a. State the multiple regression equation.

b. Interpret the regression coefficients in (a).

c. Predict the mean cost for a center city restaurant with a summated rating of 60 and construct a $95\%$ confidence interval estimate and a $95\%$ prediction interval.

d. Perform a residual analysis on the model and determine whether the regression assumptions are satisfied.

e. Is there a significant relationship between price and the two independent variable (summated rating and location) at the 0.05 level a significance?

f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.

g. Construct a $95\%$ confidence interval estimate of the population slops for the relationship between cost and summated rating.

h. Compare the slope in (b) with the slope for the simple linear regression model of Problem 13.5 on page 493. Explain the difference in the results.

i. Compute and interpret the meaning of the coefficient of multiple determination.

j. Compute and interpret the adjusted $r^2.$

k. Compare $r^2$ with the $r^2$ value computed in Problem 13.17 (b) on page 499.

l. Compute the coefficients of partial determination and interpret their meaning.

m. What assumption about the slope of cost with summated rating do you need to make in this problem?

n. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.

o. On the basis of the results of (f) and (n), which model is most appropriate? Explain.

p. What conclusions can you reach about the effect of the summated rating and the location of the restaurant on the cost of a meal?