The owners of a motel discovered that a defective product was used in its construction. It took seven months to correct the defects during which 14 rooms in the 100-unit motel were taken out of service for one month at a time. For this exercise use the data file motel.

a. Graph \(y=\) MOTEL_PCT, percentage motel occupancy, against \(x=100 R E L P R I C E\), which is the percentage of the competitor's price per room charged by the motel in question. Describe the relationship between the variables based on the graph. Is there a positive association, an inverse association, or no association?

b. Consider the linear regression MOTEL_PCT \(T_{t}=\beta_{1}+\beta_{2} 100 R E L P R I C E_{t}+e_{t}\). What sign do you predict for the slope coefficient? Why? Does the sign of the estimated slope agree with your expectation?

c. Calculate the least squares residuals from the regression in (b). Plot the residuals against TIME \(=\) \(1, \ldots, 25\) (month \(1=\) March 2003, \(\ldots\), month \(25=\) March 2005). On the graph indicate residuals when TIME \(=17,18, \ldots, 23\). These are the months of repair. Does the model overpredict or underpredict the motel's occupancy rates for those months?

d. Estimate the linear regression MOTEL_PCT \({ }_{t}=\alpha_{1}+\alpha_{2}\) REPAIR \(_{t}+e_{t}\), where REPAIR \(R_{t}=1\) for months when repairs were occurring and \(R E P A I R_{t}=0\) otherwise. What was the motel's mean occupancy rate when there were no repairs being made? What was the motel's mean occupancy rate when repairs were being made?