Question

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 con- tribute 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. *I only need help with #5,6,7 thank you

Managerial Report

1. Compute descriptive statistics and construct a scatter diagram for the data. Discuss your findings.

2. Using simple linear regression, develop an estimated regression equation that could be used to predict the number of season pass holders in a zip code given the total population of the zip code.

3. Test for a significant relationship at the .05 level of significance.

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

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

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

7. 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

Answer 1

we can solve this in excel , we enter the data in excel and then goto data > data analysis tab and select regression

1. Compute descriptive statistics and construct a scatter diagram for the data. Discuss your findings.

The results are

Population		Season Pass Holders
Mean	15738.22	Mean	128.2649
Standard Error	1028.591	Standard Error	11.83066
Median	12675	Median	59
Mode	#N/A	Mode	11
Standard Deviation	12639.54	Standard Deviation	145.3776
Sample Variance	1.6E+08	Sample Variance	21134.64
Kurtosis	1.612577	Kurtosis	1.454546
Skewness	1.306203	Skewness	1.428911
Range	61076	Range	652
Minimum	1227	Minimum	5
Maximum	62303	Maximum	657
Sum	2376471	Sum	19368
Count	151	Count	151

2. Using simple linear regression, develop an estimated regression equation that could be used to predict the number of season pass holders in a zip code given the total population of the zip code.

the regression equation is formed using the coefficients as

pass holders = -16.25 + 0.00918*Population

3. Test for a significant relationship at the .05 level of significance.

we check for the signficant F , which is almost zero (1.21755E-34)
Hence we conclude that the relationship between the variables is significant

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

the r2 of the model is 0.6374 , this means the model is able to estimate only about 63.47% variation in the data , hence the model is not a good fit

Please note that we can answer onyl 4 subparts of the question at a time , as per the answering guidelines