1. Refer to Commercial properties data. A commercial real estate company evaluates vacancy rates, square footage, rental rates, and operating expenses for commercial properties in a large metropolitan area in order to provide clients with quantitative information upon which to make rental decisions. The data are taken from 81 suburban commercial properties that are the newest, best located, most attractive, and expensive for five specific geographic areas. Shown here are the age (X1), operating expenses and taxes (X2), vacancy rates (X3), total square footage (X4), and rental rates (Y). Assume that first order linear regression model for four predictor variables with independent normal error terms is appropriate (a) Test whether there is a regression relation; use = 0.05. State the alternatives, decision rule, and conclusion. What does your test imply about B1, B2, B3 and 34? What is the P-value of the test? (b) Estimate B1, B2, B3 and 34 jointly by the Bonferroni procedure, using a 95 percent family confidence coefficient. Interpret your results. (c) Calculate R and interpret this measure. (d) The researcher wishes to obtain simultaneous interval estimates of the mean rental rates for four typical properties specified as follows: 1 2 3 4 X: 5.0 6.0 14.0 12.0 X2: 8.25 8.50 11.50 10.25 X3: 0 0.23 0.11 0 X4: 250,000 270,000 300,000 310,000 Obtain the family of estimates using a 95 percent family confidence coefficient. Employ the most efficient procedure.