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# A motel's management discovered that a defective product was used

in the motel's construction. It took seven months to correct the defects, during which time approximately 14 rooms in the 100-unit motel were taken out of service for one month at a time. The motel lost profits due to these closures, and the question of how to compute the losses was addressed. For this question, use the data in motel.sas.
(a)  The occupancy rate for the damaged motel is MOTEL_PCT, and the competitor occupancy rate is COMP_PCT. On the same graph, plot these variables against TIME. Which had the higher occupancy before the repair period? Which had the higher occupancy during the repair period (The reference lines are a Time=17 and Time=23)?
(b)  Compute the average occupancy rate for the motel and competitors when the repairs were not being made (call these  and ) and when they were being made ( and ). During the non-repair period, what was the difference between the average occupancies, these  and ? Assume that the damaged motel occupancy rate would have maintained the same relative difference in occupancy if there had been no repairs That is, assume that the damaged motel's occupancy would have been . Compute the simple estimate of lost occupancy . Compute the amount of revenue lost during the seven month period (215 days) assuming an average room rate of \$56.61 per night (Hint: use calculator not SAS or R).
(c)  Alternatively, consider a regression approach. A model explaining motel occupancy uses as explanatory variables the competitors' occupancy, the relative price (RELPRICE) and an indicator variable for the repair period (REPAIR). That is, let

Obtain the least squares estimators of parameters. Interpret the estimated coefficient, as well as their signs and significance.
(d)   Using the least squares estimate of the coefficient of REPAIR from part (c), compute an estimate of the revenue lost by the damaged motel during the repair period (215 days\$56.61). Compare this value to the "simple" estimate in part (b). Construct 95% confidence interval estimate for the estimated loss (Hint: 95% C.I.=). Is the estimated loss from part (b) within the interval estimate?