In July 1990, a rock-and-roll museum opened in Atlanta, GA. The museum was locat

Question

In July 1990, a rock-and-roll museum opened in Atlanta, GA. The museum was located in a large city block containing a variety of stores. In late July 1992, a fire 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 were entitled to more money under their insurance plan.

The argument was based on the revenues and attendance figures of an amusement park, featuring rides and other similar attractions that had opened nearby. The amusement park opened in December 1991. The two entertainment facilities were operating jointly during the last 4 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 figures for both facilities for December 1991 to October 1995 are listed in columns 1 (museum) and 2 (amusement park). During the period when the museum was closed, the data show zero attendance.

The owners of the museum argued that the weekly attendance from the 29th week of 1992 to the 16th week of 1995 should be estimated using the most current data (17th to 42nd week of 1995). The insurance company argued that the estimates should be based on the 4 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.

a. Estimate the coefficients of the simple regression model based on the insurance company’s argument. In other words, use the attendance figures for the last 4 weeks in 1991 and the next 28 weeks in 1992 to estimated 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.

b. 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.

c. Write a paragraph response to the insurance company discussing this analysis and include your recommendation about how much the insurance company should award the museum.

Week Museum Amusement Park 1 787 1379 2 1179 1396 3 4225 5332 4 1336 1477 5 2122 3717 6 1136 1663 7 2413 3573 8 1399 2086 9 1528 2503 10 1788 2553 11 3216 5239 12 2301 3646 13 1879 3041 14 1746 2841 15 2570 3468 16 2962 3851 17 3611 4332 18 3889 4706 19 4606 5933 20 4881 6259 21 4247 6232 22 2927 4545 23 2592 3705 24 2749 4337 25 4266 6968 26 3388 5600 27 4704 7005 28 6862 9305 29 6769 9396 30 8177 11755 31 10665 16131 32 9450 13080 33 0 11376 34 0 12573 35 0 14034 36 0 13806 37 0 15320 38 0 11214 39 0 6090 40 0 8146 41 0 6061 42 0 4934 43 0 4299 44 0 4977 45 0 6458 46 0 5902 47 0 6252 48 0 4704 49 0 4189 50 0 3801 51 0 3580 52 0 7665 53 0 1855 54 0 2689 55 0 3158 56 0 6119 57 0 7728 58 0 4089 59 0 1753 60 0 5535 61 0 3631 62 0 3406 63 0 3782 64 0 7193 65 0 5449 66 0 4005 67 0 3421 68 0 1445 69 0 5219 70 0 7080 71 0 7670 72 0 9794 73 0 7731 74 0 5290 75 0 5895 76 0 5347 77 0 5646 78 0 6055 79 0 10378 80 0 9782 81 0 10861 82 0 12129 83 0 14366 84 0 16186 85 0 20052 86 0 16346 87 0 16950 88 0 18048 89 0 18507 90 0 17538 91 0 13505 92 0 7427 93 0 9945 94 0 7425 95 0 7155 96 0 6310 97 0 6067 98 0 7144 99 0 7189 100 0 8007 101 0 5353 102 0 4471 103 0 4976 104 0 4280 105 0 8544 106 0 3773 107 0 3438 108 0 3919 109 0 4571 110 0 10857 111 0 3248 112 0 2297 113 0 3955 114 0 2730 115 0 3027 116 0 4380 117 0 6510 118 0 5331 119 0 4222 120 0 3808 121 0 4879 122 0 6586 123 0 5855 124 0 10811 125 0 10740 126 0 5157 127 0 6213 128 0 6132 129 0 6488 130 0 5821 131 0 6495 132 0 9895 133 0 8695 134 0 11950 135 0 12619 136 0 13908 137 0 16120 138 0 20668 139 0 16283 140 0 17167 141 0 18340 142 0 18213 143 0 17941 144 0 15011 145 0 8326 146 0 10531 147 0 7663 148 0 7864 149 0 6985 150 0 6700 151 0 8239 152 0 8245 153 0 8443 154 0 6429 155 0 5105 156 0 5179 157 0 4639 158 0 9137 159 0 3435 160 0 3497 161 0 3458 162 0 4455 163 0 13452 164 0 1797 165 0 2680 166 0 4500 167 0 3930 168 0 3449 169 0 3238 170 0 3681 171 0 6572 172 0 6109 173 0 4201 174 0 4937 175 0 7097 176 0 6400 177 0 9098 178 0 6826 179 0 9670 180 8649 8007 181 5395 5735 182 6058 6031 183 5412 5152 184 7314 5559 185 8132 8563 186 8175 8320 187 10757 10664 188 12148 11880 189 13018 12667 190 15438 15613 191 17509 18705 192 14526 14620 193 15173 15419 194 15539 15367 195 16483 16208 196 17286 16733 197 13874 12464 198 8683 8423 199 9092 9005 200 6884 7132 201 7144 6598 202 6578 6348 203 6027 5521 204 6094 6452 205 6609 6763

Explanation / Answer

I will use MS-EXCEL to carry out the regression. I will provide the link from where you can download the excel file in which I have worked at the end of the solution.

(a)

The regression output for the initial 32 weeks is given by,

The predicted total Attendance will be 785,565

(b)

The predicted total attendance in this case was 1,163,075 .

(c)

Using the first 32 weeks as the basis the predicted revenue loss of the museum will be $785,565*p

where p is the price of a ticket.

Link to download excel file :

https://www.dropbox.com/s/dg7p7l8560hqg9e/attenadnce.xlsx?dl=0

SUMMARY OUTPUT Regression Statistics Multiple R 0.99 R Square 0.98 Adjusted R Square 0.98 Standard Error 355.59 Observations 32 ANOVA df SS MS F Significance F Regression 1 2E+08 2E+08 1E+03 8E-27 Residual 30 4E+06 1E+05 Total 31 2E+08 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 16.23 114.70 0.14 0.89 -218.01 250.47 -218.01 250.47 Amusement Park 0.69 0.02 37.74 0.00 0.66 0.73 0.66 0.73

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