The Business School at Eastern College is accumulating data as a first step in t

Question

The Business School at Eastern College is accumulating data as a first step in the preparation of next year's budget development. One cost that is being looked at closely is administrative costs as a function of student credit hours. Data on administrative costs and credit hours for the past thirteen months are shown below: Administrative Credit Month Costs Hours July $ 129,457 308 August 82,095 150 September 226,262 1,445 October 216,496 986 November 257,718 1,379 December 185,230 1,206 January 219,129 1,366 February 245,511 1,491 March 210,122 1,106 April 191,966 1,132 May 249,929 1,515 June 169,884 504 July 128,677 280 Total $ 2,512,476 12,868 Average 193,267 990 The controller's office has analyzed the data and has given you the results from the regression analysis: Regression Statistics Multiple R 0.9374558 R Square 0.878823441 Adjusted R Square 0.867807391 Standard Error 19,322.13359 Observations 13 Anova df SS MS F Significance F Regression 1 29,784,194,845 29,784,194,845 79.7766331 2.25804E-06 Residual 11 4,106,793,312 373,344,846.5 Total 12 33,890,988,157 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper Intercept 94,928.44950 12,244.96300 7.75244886 8.79636E-06 67,977.46767 121,879.4313 67,977.46767 121,879.4313 X Variable 1 99.3476963 11.12294909 8.931776593 2.25804E-06 74.86625047 123.829142 74.86625047 123.829142 Based on the results of the regression analysis, the estimate of administrative costs in a month with 1,000 credit hours would be: (rounded to the nearest whole dollar) $258,895. $263,055. $194,278. $186,605.

Explanation / Answer

Result:

The Business School at Eastern College is accumulating data as a first step in the preparation of next year's budget development. One cost that is being looked at closely is administrative costs as a function of student credit hours. Data on administrative costs and credit hours for the past thirteen months are shown below: Administrative Credit Month Costs Hours July $ 129,457 308 August 82,095 150 September 226,262 1,445 October 216,496 986 November 257,718 1,379 December 185,230 1,206 January 219,129 1,366 February 245,511 1,491 March 210,122 1,106 April 191,966 1,132 May 249,929 1,515 June 169,884 504 July 128,677 280 Total $ 2,512,476 12,868 Average 193,267 990 The controller's office has analyzed the data and has given you the results from the regression analysis:

Regression Statistics Multiple R 0.9374558 R Square 0.878823441 Adjusted R Square 0.867807391 Standard Error 19,322.13359 Observations 13 Anova df SS MS F Significance F Regression 1 29,784,194,845 29,784,194,845 79.7766331 2.25804E-06 Residual 11 4,106,793,312 373,344,846.5 Total 12 33,890,988,157

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper

Intercept 94,928.44950 12,244.96300 7.75244886 8.79636E-06 67,977.46767 121,879.4313 67,977.46767 121,879.4313

X Variable 1 99.3476963 11.12294909 8.931776593 2.25804E-06 74.86625047 123.829142 74.86625047 123.829142

The regression equation y= 94,928.44950+99.3476963*x

Based on the results of the regression analysis, the estimate of administrative costs in a month with 1,000 credit hours would be: (rounded to the nearest whole dollar

$258,895.

$263,055.

Answer: $194,278.

$186,605.

When x=1000,

Y = 94,928.44950+99.3476963*1000

=194276.1

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