Chapter 14, Problem 74PS

A sample of 61 house recently listed for sale in Silver Spring, Maryland, was selected with the objectives of developing a model to predict the asking price (in $\text{\$thousands),}$ using the living space of the house (in square feet) and age (in years). The results are stored in SilverSpring.

a. Fit a multiple regression model.

b. Interpret the meaning of the slopes in this model.

c. Predict the mean asking price for a house that has 2,000 square feet and is 55 years old.

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

e. Determine the whether there is a significant relationship between asking price and the two independent variables (house size and age) at the 0.05 level of significance.

f. Determine the p-value in (e) and interpret its meaning.

g. Interpret the meaning of the coefficient of multiple determination in this problem.

h. Determine the adjusted $r^2.$

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

j. Determine the p-value in (i) and interpret their meaning.

k. Construct the $95\%$ confidence estimate of the population slope between asking price and the living space of the house. How does the interpretation of the slope here differ from that in Problem 13.76 on page 525?

l. Compute and interpret the coefficients of partial determination.

m. What conclusions can you reach about the asking price?