This data table includes the annual prices of 223 commercial leases. All of these leases provide office space in a Midwestern city in the United States.
(a) Create a scatterplot for the annual cost of the leases on the number of square feet of leased space. Does the pattern in the plot seem linear? Does the White Space Rule hint of possible problems?8
(b) Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.
(c) Interpret the summary values r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) If a business decides to expand and wants to lease an additional 1,000 square feet beyond its current lease, explain how it can use the equation obtained in part (b) to estimate the increment in the cost of its lease. Would this estimate be reliable?
(e) A row in the data table describes a lease for 32,303 square feet. The annual cost for this lease is $496,409. What is the residual for this case? Is it a good deal?
(f) Do the residuals from this regression show any patterns? Does it make sense to interpret se as the standard deviation of the errors of the ft? Use the plot of the residuals on the number of square feet to decide.