Question

Required Information 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 Number of Campers Cost to Run C amp 116 138 11.300 154 12, 280 8,000 8,530 18. 398 Required: 1. Perform a least squares regression analysis on Camp Rainbow's data 2. Using the regression output, create a cost equation (y= a + bx) for estimating Camp Rainbow's operating costs 3. Using the least squares regression results, calculate the comp's expected operating cost of 122 children attend a session

Answer 1

Requirement 1: Calculate the intercept and X variable using the regression function of Excel as follows

The path to regression function is Data −> Data Analysis−> Regression

A E F G H I Week Camp Regression ? X 138 B с Number of Cost to Ruu Campers 116 $9.330 $11,300 $12.200 $8.000 $8,530 134 $10.390 $9.830 $8.950 154 Input Input Y Range: Гок | $C$1:$C$9 1 Cancel 102 Input X Range: $B$1:$B$9 Help Labels Confidence Level: Constant is zero 95 % 108 $D$1 Output options O Output Range: New Worksheet Ply: New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

The output of above function is as follows

SUMMARY OUTPUT Regression Statistics Multiple R 0.99 R Square 0.98 Adjusted R Square 0.98 Standard Error 201.48 Observations 8.00 ANOVA df Regression Residual Total SSMSF gnificance F 1 13909620 13909620 342.647 1.6E-06 6 243567.6 40594.61 7 14153188 Intercept X Variable 1 Coefficientsandard Errt Stat 980.24 482.63 2.03 72.72 3.93 18.51 P-value Lower 95%Upper 95%ower 95.09pper 95.09 0.09 -200.71 2161.20 -200.71 2161.20 0.00 6 3.11 82.34 63.11 82.34

The intercept is $980.24 and X Variable is $72.72

Requirement 2: The cost equation is as follows

Total cost = $980.24 + ($72.72 × Number of Campers)

Requirement 3: Compute expected operating cost when 122 children attend a session as follows

Total cost = $980.24 + ($72.72 × 122)

= $9,852.08