The data in Problem 3 represent the square footage and rent for apartments in the borough of Queens and Nassau County, New York.

(a) On the same graph, draw a scatter diagram for both Queens and Nassau County apartments treating square footage as the explanatory variable, but use a different plotting symbol for Queens and Nassau County.

(b) Find the least-squares regression equation yn = b0 + b1x1 + b2x2, where x1 is square footage and x2 = 0 for Queens and x2 = 1 for Nassau County.

(c) Test the hypotheses H0: b1 = b2 = 0 versus H1: at least one of the bi ≠ 0 at the a = 0.05 level of significance.

(d) Test the hypothesis H0: b2 = 0 versus H1: b2 ≠ 0 at the a = 0.05 level of significance. What does this say about the role of location in rents in New York?

(e) Construct a 95% confidence interval for a 950-square-foot apartment in Queens.