Question

E5-11 Estimating Cost Behavior Using Least-Squares Regression [LO 5-4] Camp Rainbow offers overnight summer camp programs for children ages 10-14 every summer during June and July. Each camp session is one week and can accommodate up to 200 children. The camp is not coed, so boys attend during the odd-numbered weeks and girls attend during the even-numbered weeks. While at the camp, participants make crafts, participate in various sports, help care for the camp's resident animals, have cookouts and hayrides, and help assemble toys for local underprivileged children. The camp provides all food as well as materials for all craft classes and the toys to be assembled. One cabin can accommodate up to 10 children, and one camp counselor is assigned to each cabin. Three camp managers are on-site regardless of the number of campers enrolled. Following is the cost information for Camp Rainbow's operations last summer: Week WN- Number of Campers 170 156 134 90 166 140 Cost to Run Camp $11,550 12.060 10,600 8,310 12,880 10,880 12,510 10,000 168 00 O 118 Required: 1. Perform a least-squares regression analysis on Camp Rainbow's data. (Use Microsoft Excel or a statistical package to find the coefficients using least-squares regression. Round your answers to 2 decimal places.) Coefficients Intercept X Variable 1 This is a numeric cell, so please enter numbers only. 2. Using the regression output, create a cost equation (y = a + bx) for estimating Camp Rainbow's operating costs. Total Cost = + D Number of Campers 3. Using the least squares regression results, calculate the camp's expected operating cost if 160 children attend a session. (Round your intermediate calculations and final answer to 2 decimal places.) Total Cost

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.954803
R Square	0.911649
Adjusted R Square	0.896924
Standard Error	478.8703
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	14197187	14197187	61.91081	0.000223
Residual	6	1375901	229316.8
Total	7	15573088
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3895.386	931.0106	4.18404	0.005787	1617.285	6173.487	1617.285	6173.487
Number of Campers	50.46139	6.413218	7.868342	0.000223	34.76881	66.15397	34.76881	66.15397

1.
Intercept = $3895.39
X Variable 1 = $50.46

2.
Total Cost = $3895.30 + $50.46 x Number of Camper

3.
Total cost for 160 campers = $3895.30 + 50.46 x 160 = $11968.90