Question

Professor John Morton has just been appointed chairperson of the Finance Department at Westland University. In reviewing the department’s cost records, Professor Morton has found the following total cost associated with Finance 101 over the last several terms:

Term	Number of Sections Offered	Total Cost
Fall, last year	6		$	12,500
Winter, last year	3		$	7,500
Summer, last year	5		$	10,500
Fall, this year	2		$	6,000
Winter, this year	7		$	13,000

Professor Morton knows that there are some variable costs, such as amounts paid to graduate assistants, associated with the course. He would like to have the variable and fixed costs separated for planning purposes.

2(a). Using the least-squares regression method, estimate the variable cost per section and the total fixed cost per term for Finance 101. (Round your fixed cost and variable cost to nearest whole dollars.)

2(b). Express these estimates in the linear equation form Y = a + bX. (Round your fixed cost and variable cost to nearest whole dollars.)

3a. Assume that because of the small number of sections offered during the Winter Term this year, Professor Morton will have to offer eight sections of Finance 101 during the Fall Term. Compute the expected total cost for Finance 101. (Do not round your intermediate calculations. Round your final answer to nearest whole dollar.)

3b. Can you see any problem with using the cost formula from (2) above to derive this total cost figure?

Choose the BEST answer from the following choices:

	Prediction is based on old data.
	Prediction is out of the relevant range.
	Coefficient estimates may have high variance.
	Prediction is not guaranteed to become actual.

Answer 1

			X	Y
		Term	Number of Sections	Total Cost
		Fall, last year	6	$12,500
		Winter, last year	3	$7,500
		Summer, last year	5	$10,500
		Fall, this year	2	$6,000
		Winter, this year	7	$13,000
		Use Excel Regression
		Click "Data"
		Click "Data Analysis"
		Select "Regression"
		Input Y range:Total Cost
		Input X range:Number of sections
		Click"OK"
		You get following output:
		SUMMARY OUTPUT
		Regression Statistics
		Multiple R	0.993540609
		R Square	0.987122941
		Adjusted R Square	0.982830588
		Standard Error	402.2706868
		Observations	5
		ANOVA
			df	SS	MS	F	Significance F
		Regression	1	37214535	37214535	229.9725	0.000623
		Residual	3	485465.12	161821.7
		Total	4	37700000
			Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
		Intercept	3133.72093	481.08489	6.513863	0.00735	1602.694	4664.748	1602.694	4664.748
		X Variable 1	1470.930233	96.996076	15.16484	0.000623	1162.245	1779.615	1162.245	1779.615
	2a	Variable Cost Per Section	$1,470.93	(X Variable 1)
		Fixed Cost Per Term	$3,133.72	(Intercept)
	2b	Linear Equation;
		Y=3133.72+1470.93X
		Y=Total Cost
		X=Number of Sections
	3a	X=8
		Y=3133.72+1470.93*8=	$14,901.16
	3b	Prediction is not guaranteed to become actual.
		Prediction is based upon statistical data without logical cause and effect reasoning.
		Actual Variables influencing the costs are not considered