Chapter 14, Problem 78PS

A sample of 30 houses recently listed for sale in Silver Spring, Maryland, was selected with the objective of developing a model to predict the assessed value (in $\text{\$}$ thousands), using the size of the house (in thousands of square feet) and age (in years). The results are stored in Silver Spring.

a. Fit a multiple regression model.

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

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

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

e. Determine whether there is a significant relationship between assessed value 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-values in (i) and interpret their meaning.

k. Construct a 95% confidence interval estimate of the population slope between assessed value and the size of the house. How does the interpretation of the slope here differ from that in Problem 13.76 on page 533?

l. Compute and interpret the coefficients of partial determination. m. What conclusions can you reach about the assessed value?