on question chapter 5 probl 46P, there is a regression answer, but I was wonderi
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Question
on question chapter 5 probl 46P, there is a regression answer, but I was wondering how this was calculated with using what overhead costs and deliveries? the question states
Your company provides a variety of delivery services. Management wants to know the volume of a particular delivery that would generate $10,000 per month in operating profits before taxes. The company charges $20 per delivery.
The controller’s office has estimated overhead costs at $9,000 per month for fixed costs and $12 per delivery for variable costs. You believe that the company should use regression analysis. Your analysis shows the results to be:
Monthly overhead = $26,501 + $10.70 per delivery
Your estimate was based on the following data:
Month
Overhead Costs
Number of Deliveries
1
$142,860
11,430
2
$ 151,890
12,180
3
$192,600
15,660
4
$141,030
11,250
5
$203,490
12,780
6
$180,630
14,730
7
$159,630
12,510
8
$183,990
15,060
9
$194,430
15,450
10
$150,120
11,970
11
$154,080
12,630
12
$184,800
15,300
13
$183,120
14,580
so the regression results were
Multiple R
0.9921
R Square
0.9843
Adjusted R Square
0.9827
Standard Error
2635.7
Observations
12
Coefficients
Intercept
$9776.56
Number of deliveries
$11.69
so what was calculated to get the regression results?
Month
Overhead Costs
Number of Deliveries
1
$142,860
11,430
2
$ 151,890
12,180
3
$192,600
15,660
4
$141,030
11,250
5
$203,490
12,780
6
$180,630
14,730
7
$159,630
12,510
8
$183,990
15,060
9
$194,430
15,450
10
$150,120
11,970
11
$154,080
12,630
12
$184,800
15,300
13
$183,120
14,580
Explanation / Answer
Solution:
Notice the one observation that appears to be unusual. (This is Observation 5). Without knowing more about the reasons for high cost, we might want to treat it as an “outlier” meaning we would estimate the regression without this observation. The results of that regression are:
Regression Statistics
Multiple R
0.9921
R Square
0.9843
Adjusted R Square
0.9827
Standard Error
2635.7
Observations
12
Coefficients
Intercept
$9,776.56
Number of deliveries
$11.69
These results are much closer to the controller’s estimates.
Using the results from the “improved” regression, the cost of equation for overhead costs can be written as:
Monthly overhead = $9,776.56 + $11.69 * Number of deliveries
This implies a contribution margin per delivery of $8.31 ($20.00 - $11.69)
To earn operating profits of $10,000, the company needs approximately $2,380 [($10000 - $9,776.56)/$8.31] deliveries.
Note, however, that this level of deliveries is outside the range of the observations used to develop the regression estimates. Therefore, this estimate needs to be used with caution.
Regression Statistics
Multiple R
0.9921
R Square
0.9843
Adjusted R Square
0.9827
Standard Error
2635.7
Observations
12
Coefficients
Intercept
$9,776.56
Number of deliveries
$11.69
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