Question

The Business School at Eastern College is collecting data as a first step in the preparation of next year's budget. One cost that is being looked at closely is administrative staff as a function of student credit hours. Data on administrative costs and credit hours for the most recent 13 months follow.

Month	Administrative Costs				Credit Hours
July	$	129,301				250
August		82,613				115
September		228,580				1,392
October		216,394				1,000
November		258,263				1,309
December		184,449				1,112
January		219,137				1,339
February		245,000				1,373
March		209,642				1,064
April		191,925				1,123
May		249,978				1,360
June		170,418				420
July		128,167				315
Total	$	2,513,867				12,172
Average	$	193,374				936

The controller's office has analyzed the data and given you the results from the regression analysis, as follows.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.93339145
R Square	0.871219590
Adjusted R Square	0.859512280
Standard Error	19954.56760
Observations	13

ANOVA

	df	SS	MS	F	Significance F
Regression	1	29631603873.00	29631603873.00	74.4200000	0.0000032
Residual	11	4380032428	398184766
Total	12	34011636301.00

	Coefficients	Standard Error	T Stat	P-value	Lower 95%	Upper 95%
Intercept	96414.557	12528.42904	7.69566211	0.0000094	68839.6563	123989.4569
Credit Hours	103.5555179	12.0043317	8.62651257	0.0000032	77.1341487	129.9768871

Required:

a. In the standard regression equation y = a + bx, the letter b is best described as the:

• Constant coefficient

• Correlation coefficient

• Dependent variable

• Independent variable

• Variable cost coefficient

b. In the standard regression equation y = a + bx, the letter y is best described as the:

• Constant coefficient

• Correlation coefficient

• Dependent variable

• Independent variable

• Variable cost coefficient

c. In the standard regression equation y = a + bx, the letter x is best described as the:

• Constant coefficient

• Correlation coefficient

• Dependent variable

• Independent variable

• Variable cost coefficient

d. If the controller uses the high-low method to estimate costs, the cost equation for administrative costs is: (Do not round your intermediate calculations.)

• Cost = $69,468 + ($114 × Credit hours)

• Cost = $67,313 + ($133 × Credit hours)

• Cost = $193,374.00 × Credit hours

• Cost = $207

• Some other equation

e. Based on the results of the controller's regression analysis, the estimate of administrative costs in a month with 1,000 credit hours would be: (Round your intermediate calculations to 2 decimals.)

• 198,808

• 201,000

• 96,409

• 199,975

• Some other amount

f. The correlation coefficient (rounded) for the regression equation for administrative costs is:

• 0.871

• 0.933

• 0.859

• 0.966

• Some other amount

g. The percent of the total variance (rounded) that can be explained by the regression is:

• 93.3

• 87.1

• 85.9

• 96.6

• Some other amount

Answer 1

In a Standard Regression Equation

y = a + b x

y = dependent variable

a = intercept

x = independent variable

b = regression coefficient or slope of regression line or coefficient of independent variable

In cost determination standard regression equation

b = variable cost coefficient

a. In the standard regression equation y = a+bx, b is best defined as variable cost coefficient as when multiplied with credit hours gives the total administrative cost.

b. In the standard regression equation y = a+bx, y is best defined as dependent variable

c. In the standard regression equation y = a+bx, x is best defined as independent variable

d. If the controller uses the high-low method to estimate costs, the cost equation for administrative costs is:

Formula

Variable Cost per credit hour = (Highest Administrative Cost - Lowest Administrative Cost ) / ( Highest Credit Hours - Lowest Credit Hours)

Highest Administrative Cost and Lowest Administrative Cost are with respect to Highest Credit Hours and Lowest Credit Hours respectively

Variable Cost per credit hour = (228580-82613)/(1392-115) = $114.30

Fixed Cost = Highest Administrative Cost - Variable Cost per credit hour *Highest Credit Hours

or

Fixed Cost = Lowest Administrative Cost - Variable Cost per credit hour *Lowest Credit Hours

Fixed Cost =82613 - 114.30*115 = $69468.5

the cost equation for administrative costs = Fixed Cost + Variable Cost per credit hour *Credit Hours

So , the cost equation for administrative costs = 69468.5 + 114.30* CreditHours