Camp Rainbow offers overnight summer camp programs for children ages 10–14 every
ID: 2342254 • Letter: C
Question
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 Camp
1
154
$11,950
2
94
8,960
3
168
11,080
4
120
9,480
5
116
9,180
6
182
14,330
7
194
14,060
8
98
8,890
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
2. Using the regression output, create a cost equation (y = a + bx ) for estimating Camp Rainbow’s operating costs.
Total Cost =
+
Number of Campers
3. Using the least-squares regression results, calculate the camp’s expected operating cost if 125 children attend a session. (Round your intermediate calculations and final answer to 2 decimal places.)
Total Cost
Week
Number of Campers
Cost to Run Camp
1
154
$11,950
2
94
8,960
3
168
11,080
4
120
9,480
5
116
9,180
6
182
14,330
7
194
14,060
8
98
8,890
Explanation / Answer
1. The equation will be: y = a+bx where y = total cost and x = no. of campers x (no. of campers) y (cost) x*y x^2 154 11,950.00 1840300 23,716.00 94 8,960.00 842240 8,836.00 168 11,080.00 1861440 28,224.00 120 9,480.00 1137600 14,400.00 116 9,180.00 1064880 13,456.00 182 14,330.00 2608060 33,124.00 194 14,060.00 2727640 37,636.00 98 8,890.00 871220 9,604.00 Total 1,126.00 87,930.00 12,953,380.00 168,996.00 b = [((n*sum of x*y)-(sum of x*sum of y))/((n*sum of x^2) - (sum of x)^2)] [((8*1,2953380) - (1126*87930))/((8*168996)-(1126^2))] 103627040 99009180 4617860 1351968 1267876 84092 54.91 54.91 a (intercept) = sum of y/n - b*sum of x/n 87930/8-54.91*1126/8 3262.67 3262.67 Coefficient Intercept 3262.67 X variable 1 54.91 2. Thus total cost = 3262.67+54.91x 3. If x = 125 then total cost = 3262.67+(54.61*125) = 10126.42
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