Many variables influence the sales of existing single family homes. One of these is the interest rate charged for mortgage. Loans. The table below gives the total number of existing single family homes sold annually, y, and the average annual conventional mortgage interest rate x, for 1982 - 1997. A STATISTIX printout of the simple linear regression is provided on page 525.
a. Plot the data points on graph paper.
b. Find the least squares line relating y to x on the printout. Plot the line on your graph from part a to see if the line appears to model the relationship between y and x.
c. Do the data provide sufficient evidence to indicate that mortgage interest rates contribute information for the prediction of annual sales of existing single family homes? Use α = .05.
d. Locate r2 and interpret is value.
e. A 95% confidence interval for the mean annual number of existing single-family homes sold when the average annual mortgage interest rate is 8.0% is shown next to "Lower/ Upper Fitted Bound" on the printout. Interpret this interval.
f. A 95% prediction interval for the annual number of existing single-family homes sold when the average annual mortgage interest rate is 8.0% is shown next to"Lower1Upper Predicted Bound" on the printout. Interpret this interval
g. Explain why the widths of the intervals found in parts e and f differ.