Question

E5-11 Estimating Cost Behavior Using Least-Squares Regression [LO 5-4) Camp Rainbow offers Ovemight 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 Number of Campers 196 138 144 Cost to Run Camp $13,170 10.010 11,110 8.120 10.950 11,770 12.930 12,460 132 136 160 158 00 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

Answer 1

Answer 1:

Intercept X Variable 1 Coefficients 3,671.44 52.71

Working:

Using statistical package 'Regression' in Data Analysis tool of Excel, we get the below summary output of regression analysis.

The intercept and X variable values are highlighted.

Week Number of Campers Cost to Run Camp 196 $13,170 138 $10,010 144 $11,110 96 $8,120 132 $10,950 136 $11,770 160 $12,930 158 $12,460 SUMMARY OUTPUT Regression Statistics Multiple R 0.897411093 R Square 0.80534667 Adjusted R Square 0.772904448 Standard Error 798.5026293 Observation ANOVA df Regression Residual SS MSF Significance F si 15827961.31 15827961.31 24.82402951 0.002495816 3825638.694 637606.449 19653600 Total Intercept Number of Campers Coefficients 3671.443118 52.71418539 Standard Error t Stat P-value 1559.879903 2.353670376 0.056772937 10.58013868 4.982371876 0.002495816 Lower 95% Upper 95% Lower 95.0% Upper 95.0% -145.4455038 7488.33174 -145.4455038 7488.33174 26.82551868 78.60285211 26.82551868 78.60285211

Answer 2:

Cost Equation is as follows:

Total Cost = 3,671.44 + 52.71 * Number of Campers

Answer 3:

Total Cost = $12,632.14

Working:

Cost equation is:

Total cost = 3671.44 + 52.71 * Number of campers

= 3671.44 + 52.71 * 170

= $12,632.14