Question

In: Statistics and Probability

Buckeye Creek Amusement Park is open from the beginning of May to the end of October....

Buckeye Creek Amusement Park is open from the beginning of May to the end of October. Buckeye Creek relies heavily on the sale of season passes. The sale of season passes brings in significant revenue prior to the park opening each season, and season pass holders contribute a substantial portion of the food, beverage, and novelty sales in the park. Greg Ross, director of marketing at Buckeye Creek, has been asked to develop a targeted marketing campaign to increase season pass sales. Greg has data for last season that show the number of season pass holders for each zip code within 50 miles of Buckeye Creek. he has also obtained the total population of each zip code from the U.S. Census bureau website. Greg thinks it may be possible to use regression analysis to predict the number of season pass holders in a zip code given the total population of a zip code. If this is possible, he could then conduct a direct mail campaign that would target zip codes that have fewer than the expected number of season pass holders.

1. Did the estimated regression equation provide a good fit?

2. Use residual analysis to determine whether the assumed regression model is appropriate.

3. Discuss if/how the estimated regression equation should be used to guide the marketing campaign.

4. What other data might be useful to predict the number of season pass holders in a zip code?

ZIP Code

 Population Season Pass Holders
45220 14171 224
45219 17576 42
45225 13437 15
45217 5731 78
45214 9952 19
45232 6913 28
45223 13349 83
45229 15713 75
45206 11353 69
45202 15105 83
45203 3411 9
45207 8233 8
41074 5566 36
41073 6193 63
45224 21043 207
41071 21596 133
45205 21683 102
45204 6642 36
41016 5603 42
45216 9028 55
45212 22356 207
41011 25849 193
41014 7913 41
45237 21137 86
45208 18236 424
45211 33968 342
45239 26485 269
41075 15868 236
45209 8941 111
45226 5029 84
45238 42737 564
45231 39939 361
45213 11683 153
45215 28915 308
45218 3917 54
41017 40218 493
41076 14779 176
45251 22887 205
45227 18431 215
45247 20372 357
41015 22298 189
45248 22880 380
45236 21823 310
45240 27033 142
45246 13522 100
45230 25763 423
45233 14175 244
45252 4799 58
41018 29001 244
45243 14755 303
45241 25623 299
45014 44178 307
45242 20015 377
45244 26316 448
41059 2266 22
41048 12597 214
41051 18730 323
45255 22552 307
45174 2072 52
41042 50429 440
45002 13298 184
45015 12504 47
45069 46264 561
45052 3770 52
45249 13432 154
41001 16982 164
41005 20892 209
45011 62303 496
45245 17701 189
41091 17372 226
45013 51730 286
45150 31179 316
41094 9748 106
45030 16386 192
45140 52874 657
41063 3662 19
45040 51183 549
45102 22009 217
45039 21398 278
41007 3215 26
45053 3441 25
45157 10312 72
45050 6988 80
41080 2114 11
45067 12507 62
45034 1227 11
45103 29874 267
47025 21986 154
45044 49621 322
41030 7280 35
41092 3198 18
45065 5194 35
41033 1712 11
47060 6910 38
41006 4835 19
45122 12550 59
45042 28821 91
45056 28811 88
45036 36066 225
45064 2376 9
47040 5242 10
45153 2132 10
45152 9686 101
47022 2740 17
47001 10370 36
45162 2900 11
45005 31944 93
41035 9671 54
45106 12675 61
45176 8485 47
45311 7381 10
41043 2968 7
45327 7961 13
41040 7249 14
45066 23119 129
41097 6854 22
45054 1730 12
41095 4218 11
45120 3774 20
45342 31929 55
47032 3628 10
45107 9608 40
47012 10579 23
45130 4202 17
45118 4239 23
41086 1602 5
47018 4435 12
45458 26281 75
45449 19237 15
45068 11293 28
47041 5544 18
45113 4118 16
45154 8093 41
45320 15282 8
45459 26744 39
47031 5179 12
41004 4311 9
41003 2397 5
41010 3321 5
41002 2104 6
45429 25537 39
45305 11159 16
45409 13554 9
45419 15782 33
45121 8919 26
45440 19463 25
45420 24393 20
45410 17025 7
45430 7137 7
45403 16794 8
45142 4973 10

Solutions

Expert Solution

1. Did the estimated regression equation provide a good fit?

The p-value for the significance test of slope is 0.000 and less than 0.05 significance level. Hence, we can conclude that Population has statistically significant effect on Season Pass Holders. Hence, we can conclude that the estimated regression equation provides a good fit.

2. Use residual analysis to determine whether the assumed regression model is appropriate.

From the scatter plot of the serial number of the observation VS residulas does not a random pattern. Hence, the assumption of random on residulas is violated.

From the above scatter plot between the residulas and explanatory variable population, the variation of the residuals is increased when increasd the value of population and has a funnenl shape relationship. So, the assumtion of independence between the residulas and explanatory variable is violated.

Hence, the residual analysis determines that the assumptions of the regression model are not appropriate.

3. Discuss if/how the estimated regression equation should be used to guide the marketing campaign.

Ans: By suning this regression equation we can estimate the value of Season Pass Holders for a ZIP Code when we know the population of this ZIP Code.

4. What other data might be useful to predict the number of season pass holders in a zip code?

Ans: Only 63.7% percent variation of the dependent variable season pass holders can be explained by the explanatory variable Population .Hence, other data might be useful to predict the number of season pass holders in a zip code.

orchestra answered 1 year ago
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