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 54.91

2. Using the regression output, create a cost equation (y = a + bx ) for estimating Camp Rainbow’s operating costs.

	Total Cost = + 54.91 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

Answer 1

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