This document discusses statistical cost estimation techniques, including variable costs, fixed costs, and mixed costs. It explains how to use the scattergraph method and regression analysis to derive a total cost equation and estimate mixed costs. Specifically, it discusses using regression to interpret results like the correlation coefficient, coefficient of determination, and t-statistic. It provides an example of using multiple regression with two predictor variables and interpreting those results. Finally, it discusses potential problems that can occur with regression data like curvilinear costs, outliers, spurious relations, and violating assumptions.

1. Cost Behavior

2. Cost Behavior
• Variable
• Fixed
• Mixed

3. Estimating Mixed Costs
• Scattergraph method
• Goal: Derive TC equation
– Hi-Low analysis
– Regression
– Multiple Regression

4. Interpreting Regression
LO5
Interpret the results of regression output.
F
V
Y
= Intercept
Y =
Slope
F
+ V
X
X

5. Interpreting Regression, Continued. . .
Correlation
coefficient
“R” measures the linear relationship between
variables. The closer R is to 1.0 the closer the
points are to the regression line. The closer R is to
zero, the poorer the regression line.
Coefficient of
determination
“R2” The square of the correlation coefficient. The
proportion of the variation in the dependent
variable (Y) explained by the independent
variable(s)(X).
T-Statistic
The t-statistic is the value of the estimated
coefficient, b, divided by its standard error.
Generally, if it is over 2, then it is considered
significant. If significant, the cost is NOT totally
fixed.

6. Interpreting Regression, Continued. . .
Correlation Coefficient
Coefficient of Determination
T-Statistic
.91
A linear relationship does exists between repair hours and overhead costs.
.828
82.8% of the changes in overhead costs can be explained by changes
in repair-hours.
10.7 & 7.9
Both have t-statistics that are greater than 2, so the cost is not totally
fixed.
Estimate 3C’s overhead with 520 repair hours.

7. Multiple Regression
Multiple Regression:
When more than one predictor (x)
is in the model.
Is repair-hours the only activity that drives
overhead costs at 3C?
Predictors:
X1: Repair-hours
X2: Parts Cost
Equation:
TC = VC(X1) + VC(X2) + FC

8. Multiple Regression, Continued. . .
3C Cost Information
Month
OH Costs
Repair-Hours (X1)
Parts (X2)
1
$9,891
248
$1,065
2
$9,244
248
$1,452
3
$13,200
480
$3,500
4
$10,555
284
$1,568
5
$9,054
200
$1,544
6
$10,662
380
$1,222
7
$12,883
568
$2,986
8
$10,345
344
$1,841
9
$11,217
448
$1,654
10
$13,269
544
$2,100
11
$10,830
340
$1,245
12
$12,607
412
$2,700
13
$10,871
384
$2,200
14
$12,816
404
$3,110
15
$8,464
212
$ 752

9. Multiple Regression Output
Interpret results and estimate total costs with 520 repair hours and
$3500 parts costs

10. Statistical Cost Estimation Using Regression Analysis
Statistical procedure to determine the
relationship between variables.
High-Low Method
Regression
Uses two data points.
Uses all the data points.
3C Overhead

11. Implementation Problems
LO6
Identify potential problems with regression data.
1. Curvilinear costs
2. Outliers
3. Spurious relations
Curvilinear costs
4. Assumptions
Identify relevant range
Analyze relevant range
Relevant
Range

12. ICE
Month
Customer Accts
Paychecks Proc
Acct Svc Costs
1
325
1029
63800
2
310
993
68900
3
302
1268
64000
4
213
1028
61300
5
222
984
61600
6
214
712
50800
7
131
762
51020
8
123
739
54300
9
115
708
50500
10
296
1232
64800
11
213
978
58000
12
222
929
57500
13
217
1059
62200
14
132
942
54900
15
300
1299
71530
16
315
1283
64800
3650
15945
959950
Totals
Required:
Based on customer accounts, paychecks processed
HiLo Analysis
Regression
Multiple Regression