Chapter 14, Problem 40PS

A real estate association in a suburban community would like to study the relationship between the size of a single-family house (as measured by the number of rooms) and the selling price of the house $\text{(in}\text{\$thousand)}$ . Two different neighborhoods are included in the study, one on the east side of the community (= 0) and the other on the west side (= 1). A random sample of 20 houses was selected, with the results stored in Neighbor. For (a) through (k), do not include an interaction team.

a. State the multiple regression equation that predicts the selling price, based on the number of rooms and the neighbourhood.

b. Interpret the regression coefficients in (a).

c. Predict the mean selling price for a house with nine rooms that is located in an east-side neighbourhood. Construct a $\text{95\%}$ confidence interval estimate and a $\text{95\%}$ prediction interval.

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

e. Is there a residual analysis on the model and determine whether the regression assumptions are valid.

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 and interpret a $\text{95\%}$ confidence interval estimate of the population slope for the relationship between selling price and number of rooms.

h. Construct and interpret a $\text{95\%}$ confidence interval estimate of the population slope for the relationship between selling price and neighbourhood.

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

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

k. What assumption do you need to make about the slope of selling price with number of rooms?

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

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

n. What conclusions can the real estate association reach about the effect of the number of rooms and neighbourhood on the selling price of homes?