13.76 You want to develop a model to predict the asking price of homes based on their size. A sample of 61 single-family houses listed for sale in Silver Spring, Maryland, a suburb of Washington, DC, is selected to study the relationship between asking price

(in $thousands) and living space (in square feet), and the data are collected and stored in Silver Spring Homes . (Hint: First determine which are the independent and dependent variables.)

a. Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.

b. Interpret the meaning of the Y intercept, b0, and the slope, b1, in this problem.

c. Use the prediction line developed in

(a) to predict the mean asking price for a house whose living space is 2,000 square feet.

d. Determine the coefficient of determination, r2, and interpret its meaning in this problem.

e. Perform a residual analysis on your results and evaluate the regression assumptions.

f. At the 0.05 level of significance, is there evidence of a linear relationship between asking price and living space?

g. Construct a 95% confidence interval estimate of the population slope.

h. What conclusions can you reach about the relationship between the living space and asking price?