Question

3. An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville, which has a population of 70,230 people and a median household income of $31,500. The analyst identified 24 towns in the region that already had public swimming pools. She conducted a telephone interview with the recreation department in each town to find out what fee it charged per visit (FEE) and how many visits it had during the most recent summer season (VISITS). In addition, she was able to find each town’s population (POP) and median household income (INCOME) in the most recent census. Her data are as follows:

Town	Visits	Fee ($)	Income ($)	Population
1	110	$0.00	20,600	36,879
2	220	$0.00	33,400	64,520
3	380	$0.00	39,700	104,123
4	210	$0.00	32,600	103,073
5	160	$0.00	24,900	58,386
6	320	$0.25	38,000	116,592
7	190	$0.25	26,700	49,945
8	120	$0.25	20,800	79,789
9	180	$0.25	26,300	98,234
10	275	$0.50	35,600	71,762
11	350	$0.50	38,900	40,178
12	130	$0.50	21,700	22,928
13	305	$0.50	37,900	39,031
14	260	$0.50	35,100	44,685
15	290	$0.50	35,700	67,882
16	140	$0.75	22,900	69,625
17	335	$0.75	38,600	98,408
18	100	$0.75	20,500	93,429
19	365	$1.00	39,300	98,077
20	170	$1.00	25,800	104,068
21	150	$1.25	23,800	117,940
22	245	$1.50	34,000	59,757
23	200	$1.50	29,600	88,305
24	230	$2.00	33,800	84,102

1. Show how the analyst could use these data to predict the gross benefits of opening a public swimming pool in Dryville and allowing free admission.
2. Predict gross benefits if admission is set at $1.00

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9713
R Square	0.9435
Adjusted R Square	0.9350
Standard Error	21.7959
Observations	24
ANOVA
	df	SS	MS	F	Significance F
Regression	3	158722.7428	52907.58093	111.3701308	1.19038E-12
Residual	20	9501.215552	475.0607776
Total	23	168223.9583
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-147.0703	23.2596	-6.3230	0.0000	-195.5889	-98.5517
Fee ($)	-9.2289	8.5879	-1.0746	0.2953	-27.1429	8.6851
Income ($)	0.0121	0.0007	18.0862	0.0000	0.0107	0.0135
Population	0.0001	0.0002	0.5970	0.5572	-0.0003	0.0005

a. The data can be used to run regression analysis (results are as above) by setting Visits as dependent variable, Fee, Income and population as independent variable. The regression equation is of the form,
Visists = Intercept+a*Fee+b*Income+c*population
For free admission, Visits = -147.07-9.23*0+0.012*31500+0.0001*70230=237.95

b. For fee of $1,
Visits = -147.07-9.23*1+0.012*31500+0.0001*70230 = 228.72