Question: In July 1990, a rock-and-roll museum opened in Atlanta, Georgia. The museum was located in a large city block containing a variety of stores. In late July 1992, a fire that started in one of these stores burned the entire block, including the museum. Fortunately, the museum had taken out insurance to cover the cost of rebuilding as well as lost revenue.

As a general rule, insurance companies base their payment on how well the company performed in the past. However, the owners of the museum argued that the revenues were increasing, and hence they are entitled to more money under their insurance plan. The argument was based on the revenues and attendance figures of an amusement park that was opened nearby, featuring rides and other similar attractions. The amusement park opened in December 1991. The two entertainment facilities were operating jointly during the last four weeks of 1991 and the first 28 weeks of 1992 (the point at which the fire destroyed the museum). In April 1995, the museum reopened with considerably more features than the original one.

The attendance for both facilities for December 1991 to October 1995 is presented in the file MUSEUM.xlsx. During the period when the museum was closed, the data show zero attendance.

Both the museum owners and the insurance company agreed that the two attractions would have attendance that was highly correlated, and therefore that the attendance at the amusement park could form a guide to measure the lost revenue. That is, both parties agreed that an equation relating the museum attendance to the amusement park attendance could be used to estimate the missing lost attendance at the museum.

The owners of the museum argue that the weekly attendance from the twenty-ninth week of 1992 to the sixteenth week of 1995 should be estimated using the most current data (seventeenth to forty-second week of 1995). The insurance company argues that the estimates should be based on the four weeks of 1991 and the 28 weeks of 1992, when both facilities were operating and before the museum reopened with more features than the original museum.

1. Estimate the coefficients of the simple regression model based on the insurance company's argument. That is, use the attendance figures for the last four weeks in 1991 and the next 28 weeks in 1992 to estimate the coefficients. Then, use the model to calculate point predictions for the museum's weekly attendance figures when the museum was closed. Calculate the predicted total attendance.
2. Repeat part a) using the museum's argument. That is, use the attendance figures after the reopening in 1995 to estimate the regression coefficients and use the equation to predict the weekly attendance when the museum was closed. Calculate the total attendance that was lost because of the fire.
3. In your opinion, which figure should be used to calculate how much the insurance company should award the museum? How should that compensation be determined?

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