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Chapter 8 - Cost Estimation
Case 8-5 Predicting the Effect of Poverty on High School Graduation Rate
High School graduation rates are a key measure of economic development and potential for economic
growth. The data below show the graduation rates and the percentage of children in poverty for each of
the states in the U.S. The graduation rate is for the school year 2004-2005 and the poverty data is for
2007. The data is from the U.S. Census Bureau and is reported in the November 24, 2008 issue of
Business Week, p 15.
Required:
1. Use regression analysis to answer the question whether there might be a causal relationship
between poverty level and graduation rates.
2. Critically examine the regression results you have developed. Include in your answer a
consideration of the data used and a consideration of potential additional variables that could be
used to predict graduation rates.
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Chapter 8 - Cost Estimation
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Chapter 8 - Cost Estimation
Regression Analysis
1. The regression results for the above data, shown in the Excel spreadsheet below, indicate that
there is a strong statistical relationship between percentage of children in poverty and graduation
rate; as expected the relationship is negative, that is, the higher the poverty rate, the lower the
graduation rate.
2. The t statistic for the poverty variable is strongly significant, but other measures are not good.
The R square of 17% is quite low, indicating a poorly fitting model. Also, the standard error of
the estimate is large, at 7.15, relative to the average value of the dependent variable. So the
model can be used to show that a likely relationship between the variables exists, but the nature
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Chapter 8 - Cost Estimation
Case 8-6: University Cost Forecasting
1. The following are four different regression models that were run on the Western
University data. See below for the regression results and an overall evaluation that
follows.
Regression One: Students Enrolled
Plot of Regression One
Regression Two: Sections Taught
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Chapter 8 - Cost Estimation
Plot of Regression Two
118,377,586
118,083,424
117,622,521
115,928,777
118,591,407
120,042,361
117,352,268
116,889,599
120,335,311
122,635,639
122,954,610
117,160,456
127,600,050
127,291,099
129,436,179
123,683,762
123,192,014
125,798,899
119,002,174
128,408,000
125,508,964
128,577,777
126,856,310
127,352,245
Total Costs
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Chapter 8 - Cost Estimation
Regression Three: Number of Courses Listed
Plot of Regression Three
115,928,777
122,954,610
123,192,014
117,160,456
117,352,268
120,335,311
116,889,599
127,291,099
117,622,521
118,591,407
123,683,762
118,083,424
119,002,174
118,377,586
120,042,361
122,635,639
127,600,050
128,408,000
128,577,777
126,856,310
125,798,899
129,436,179
127,352,245
125,508,964
Total Costs
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Chapter 8 - Cost Estimation
Regression Four: Courses listed, Sections Taught, and Students Enrolled
Overall Evaluation:
Each of the simple regressions on the three independent variables (regressions one, two,
and three) are significant at p < .01, and each have coefficients for the independent variable that
are in the expected direction and of a plausible amount. The adjusted R square for each
regression is low, however. Note from the plots for each regression shown above that the data
points are well scattered in each regression. This means that each of the regressions has a
limited amount of goodness of fit and limited reliability as a measure of the relationship between
each of these variables and the University’s costs. As such, predictions made using any of the
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Chapter 8 - Cost Estimation
Adjusted R-
Square
Independent
Variable Coefficient P-value
Regression One .3105 Students enrolled $2,323 .0028
Regression Two .4761 Sections taught $6,641 .0001
Regression Three .3032 Courses listed $24,040 .0031
The multiple regression, regression four, includes all three independent variables and has
higher R square (.6371), and lower standard error of the estimate ($2,698) than any of the prior
regression, this indicates some degree of multicollinearity between this variable and one or both
of the other variables. However, because of the greatly improved reliability and precision, the
multiple regression model is the best choice for predicting University costs.
2. The above analysis can be compared to activity-based costing because it takes a multiple
cost driver approach to forecasting total cost.
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Chapter 8 - Cost Estimation
Teaching Strategy for Reading
“How to Find the Right Bases and Rates”
This article shows an actual application of regression analysis for determining multiple overhead
rates using the spreadsheet software. The article explains the interpretation of the R-squared and t-values
and provides a good discussion of when regression analysis is useful.
Discussion Questions:
1. What is regression analysis used to accomplish in this article?
The regression analysis is used to determine the best cost drivers to use when using multiple overhead
2. What are the steps to perform a simple regression analysis?
The use of regression, as explained in this article, requires a spreadsheet program such as EXCEL, and
computing applications (spreadsheets) to assist accounting tasks such as the choice of cost drivers.
3. What does Table 4 tell you? Which cost driver would you pick for each cost typemaintenance,
packaging, materials handling, storage, and production scheduling?
Table 4 provides the information we need to determine which single cost driver provides the best
fit for each cost type:
maintenance: machine hours
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