Chapter 13, Problem 76PS

You want to develop a model to predict the asking price of homes based on their size. A sample of single-family houses listed for sale in Silver Spring, Marland, a suburb of Washington, DC, is selected to study the relationship between asking price (in $\text{\$thousands}$ ) and living space (in square feet), and the data is collected and stored in SilverSpring. (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 $b_0$ and $b_1.$

b. Interpret the meaning of the $Y$ intercept, $b_0$ , and the slope, $b_1,$ 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 $r^{\text{2}},$ 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?