Chapter 14, Problem 76PS

A sample of 61 houses recently listed for sale in Silver Spring, Maryland, was selected with the objective of developing a model to predict the taxes (in $\text{\$}$ ) based on the asking price of house $\text{(in \$thousand)}$ and the age of the house (in years) (stored in SilverSpring):

a. State the multiple regression equation.

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

c. Predict the mean taxes for a house that has an asking price of $\text{\$400,000}$ and is 50 years old.

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

e. Determine whether there is a significant relationship between taxes and the two independent variables (asking price 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 a $95\%$ confidence interval estimate of the population slope between taxes and asking price. How does the interpretation of the slope here differ from that of problem 13.77 on page 525?

l. Compute and internet the coefficients of partial determination.

m. The real estate assessor’s office has been publicly quoted as saying that the age of a house has no bearing on its taxes. Based on your answer to (a) through (l), do you agree with this statement? Explain.