Chapter 13, Problem 76PS

You want to develop a model to predict the assessed value of homes based on their size. A sample of 30 single-family houses listed for sale in Silver Spring, Maryland, a suburb of Washington, DC, is selected to study the relationship between assessed value $\left(\text{in \$ thousands}\right)$ and size (in thousands of square feet), and the data is collected and stored in SilverSpring.

a. Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coefficients $b_{\text{0}}\text{ and }{b}_1$ .

b. Interpret the meaning of the Y intercept, $b_{\text{0}}\text{,}$ and the slope, $b_1,$ in this problem.

c. Use the prediction line developed in (a) to predict the mean assessed value for a house whose size is 2,000 square feet.

d. Determine the coefficient of determination, $r^2,$ 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 assessed value and size?

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

h. What conclusions can you reach about the relationship between the size of the house and its assessed value?