Question

Please answer problem 2. An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville, which has a population of 50,000 people and a median household income of $40,000. The analyst identified 20 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. The data are provided at the bottom of the question.

For question 1, use Excel and the data provided to estimate the regression coefficients for the equation

VISITS = a0 + a1*FEE + a2*INCOME + a3*POP

Question 1 Answer: VISITS = 151916.376 - 16921.188*FEE - 0.206*INCOME + 0.565*POP

For problem 2, use your answers to question 1 in combination with information on Dryville’s population and median household income to calculate the intercept and slope of the inverse demand curve for the Dryville pool and to calculate gross social benefit. The inverse demand curve is written as

FEE = b0 + b1*VISITS

What is the intercept of the inverse demand curve? (For your answer, include twodigits after the decimal point.)

b0 =

What is the slope of the inverse demand curve? (For your answer, include sixdigits after the decimal point.)

b1 =

What is the estimated gross social benefit of the Dryville public swimming pool project? (Do not include a comma or decimal point in your answer.)

GSB = $

Please upload a document showing your work (regression output, math calculations, and graphs) so I can assign partial and full credit as appropriate.

Visits Income ($) Population Fee ($) $0.00 168,590 20,600 179,599 198,595 206,662 209,995 172,018 190,802 197,019 186,515 152,679 158,056 157,424 179,490 164,657 184,428 174,510 187,820 196,318 166,694 161,716 $0.00 $0.00 $0.00 $0.25 $0.25 $0.25 $0.25 $0.50 $0.50 $0.50 $0.50 $0.50 $0.75 $0.75 $1.00 $1.00 $1.25 $1.50 $1.50 33,400 39,700 32,600 38,000 26,700 20,800 26,300 35,600 38,900 37,900 35, 100 35,700 22,900 38,600 39,300 25,800 23,800 34,000 29,600 36,879 64,520 104, 123 103,073 116,592 49,945 79,789 98,234 71,762 40,178 39,031 44,685 67,882 69,625 98,408 98,077 104,068 117,940 59,757 88,305 15 16

Answer 1

What is the intercept of the inverse demand curve? (For your answer, include twodigits after the decimal point.)

b0 = 2.20

What is the slope of the inverse demand curve? (For your answer, include sixdigits after the decimal point.)

b1 = -0.000009

What is the estimated gross social benefit of the Dryville public swimming pool project? (Do not include a comma or decimal point in your answer.)

GSB = $No info is given for this one.

Visits	Fee	Income	Population
168590	0	20600	36879
179599	0	33400	64520
198595	0	39700	101123
206662	0	32600	103073
209995	0.25	38000	116592
172018	0.25	26700	49945
190802	0.25	20800	79789
197019	0.25	26300	98234
186515	0.5	35600	71762
152679	0.5	38900	40178
158056	0.5	37900	39031
157424	0.5	35100	44685
179490	0.5	35700	67882
164657	0.75	22900	69625
184428	0.75	38600	98408
174510	1	39300	98077
187820	1	25800	104068
196318	1.25	23800	117940
166694	1.5	34000	59757
161716	1.5	29600	88305

	r²	0.104
	r	-0.322
	Std. Error	0.466
	n	20
	k	1
	Dep. Var.	Fee
ANOVA table
Source	SS	df	MS	F	p-value
Regression	0.45240909	1	0.45240909	2.08	.1660
Residual	3.90696591	18	0.21705366
Total	4.35937500	19
Regression output				confidence interval
variables	coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	2.20
Visits	-0.000009	0.00000631	-1.444	.1660	-0.00002235	0.00000414