Summer 2004
Stat 328 Exam II
Prof. Vardeman
This exam concerns the analysis of some data taken from Data Analysis Using Regression Models:
The Business Perspective by Frees. They come originally from a study by Schmit and Roth reported in
the paper “Cost Effectiveness of Risk Management Practices” published in The Journal of Risk and
Insurance. 73 risk managers of large companies (from a larger number originally sent questionnaires)
returned questionnaires giving information about the risk management practices of their organizations.
The response variable of basic interest is firmcost , the total property and casualty premiums and
uninsured losses expressed as a percentage of total company assets. Some preliminary analysis
suggested that for modeling purposes, a more convenient version of the response variable is
costlog = log10 ( firmcost )
and our discussion will use this variable. (Note that “undoing” the logarithm transform,
firmcost = 10costlog .) Potential explanatory variables are both “financial” and “attitudinal.” Financial
predictor variables available for analysis are
assume = per occurence retention amount as a percentage of total assets
cap
= a 0-1 dummy variable indicating whether the company owns a captive
insurance company
sizelog = the logarithm of firm total assets
indcost = a measure of the firm's industry risk
Attitudinal predictor variables available for analysis are
central = a measure of the centralization of decisions about how
much risk to retain
soph = a measure of the technical sophistication (the importance
of analytical tools like regression) in comapny risk mangement
Further, for modeling purposes, we will also consider the predictor variable
2
indcost -squared = ( indcost )
There is a logical “gotcha” in the analysis of data like these that come from a survey with a low
response rate. That is the very real possibility that “non-responders” are unlike “responsders” and
researchers try to assess the degree to which this is the case (and one can only take any analysis as
relevant to “responders” and “similar” subjects). We’ll ignore the issue for the purposes of this exam
and suppose that data used here are representative of all large US firms.
Accompanying this exam are a data table and JMP reports from various analyses of the survey data.
Use them as you choose the best single answer to each of the following 25 multiple choice
questions. After you have finished this exam, transfer your answers to the answer sheet and turn in the
answer sheet, this exam, and the JMP reports, all with your name written plainly on them.
1
There is evidence on the JMP reports of multicollinearity among the basic predictors (for the time
being, ignore indcost -squared ).
1.
a)
b)
c)
d)
e)
From the evidence available to you, which two predictors seem most strongly related?
assume, cap
assume, sizelog
assume, indcost
sizelog , cap
central , soph
2.
a)
b)
c)
d)
From the evidence available to you, large (as measured by sizelog ) firms seem to
assume/retain relatively low risk and have low sophistication scores.
assume/retain relatively high risk and have low sophistication scores.
assume/retain relatively low risk and have high sophistication scores.
assume/retain relatively high risk and have high sophistication scores.
sizelog seems to be the best single predictor of the response variable costlog . Until further notice
consider a simple linear regression analysis of y = costlog as a function of x = sizelog .
3.
a)
b)
c)
d)
e)
What do you estimate to be the standard deviation of costlog for a fixed value of sizelog ?
.050
.170
.405
.413
.423
4. What are 95% confidence limits for the increase in mean costlog that accompany a 1 unit increase
in company sizelog ?
a) 3.68 ± 3.68
b) 3.68 ± .85
c) −.35 ± .35
d) −.35 ± .10
(
e) ( 3.68 + ( −.35 ) ⋅1) ± 2.00 SE µˆ
)
5. Is there clear evidence that mean costlog changes with sizelog ?
a) Yes. The p -value for testing H 0 :β1 = 0 in the SLR model is less than .05.
b) No. The p -value for testing H 0 :β1 = 0 in the SLR model is less than .05.
c) Yes. The p -value for testing H 0 :β1 = 0 in the SLR model is more than .05.
d) No. The p -value for testing H 0 :β1 = 0 in the SLR model is more than .05.
2
6. What are 95% confidence limits for the mean costlog for companies with sizelog = 10 ?
a) ( −.68,1.02 )
b)
c)
d)
e)
( −.02,.36 )
(.04,1.70 )
(.77,.98)
.17 ± 2.00 (.413)
7. For a certain value of sizelog , SE µˆ = .07 (used for making confidence limits for µ y|x ). The
corresponding value of SE yˆ (used for making prediction limits for ynew , a new value of costlog at that
value of sizelog ) is closest to
a) .07
b) .17
c) .42
d) .48
e) 1.00
8. For a certain value of sizelog and confidence level, prediction limits for an additional value of
costlog are .87 ± .70 . Corresponding prediction limits for firmcost = 10logcost
a) are 10.17 and 101.57 , i.e. 1.48 and 37.15
b) are 10.87 − 10.70 and 10.87 + 10.70 , i.e. 2.40 and 12.43
c) can not be determined from the given information
d) None of a) through c) are correct.
9. Suppose that an additional survey form was returned incomplete, but carrying the information that
firmcost = 10 so that costlog = 1 and that you must estimate the company’s value of sizelog . What is
an estimate based on the least squares line?
a) 5.6
b) 6.6
c) 7.6
d) 8.6
e) 9.6
10. Case number 15 stands out on the plot of costlog versus sizelog . As a matter of fact, JMP
calculations not represented in the reports available to you show that the case has a “hat” value that is
not particularly large, but has the biggest “Cook’s D” in the data set for this simple linear regression
analysis. This reflects the facts that for firm number 15
a) sizelog is extreme, and the residual is large
b) sizelog is moderate, and the residual is large
c) sizelog is extreme, and the residual is moderate
d) sizelog is moderate, and the residual is moderate
3
In the search for a good model for costlog , Vardeman ran the “All Possible Models” routine in JMP.
Below are some summary values for “best” (largest R 2 ) models of each “size” (number of predictors).
Number
of
Predictors
Predictors
sizelog , indcost , ( indcost ) ,
R2
s = RMSE
p
Cp
.5841
.3605
8
8.00
10.54
8.45
.5841
.3578
7
6.00
10.17
8.45
.5826
.3558
6
4.24
10.00
8.48
PRESS
SSE
2
7
central , assume, soph, cap
sizelog , indcost , ( indcost ) ,
2
6
central , assume, soph
sizelog , indcost , ( indcost ) ,
2
5
central , assume
sizelog , indcost , ( indcost ) ,
2
.5750
.3563
5
3.42
10.16
8.63
3
central
2
sizelog , indcost , ( indcost )
.5655
.3577
4
2.90
10.01
8.83
2
1
sizelog , indcost
sizelog
.5150
.4052
.3752
.4125
3
2
8.80
23.96
4
10.98 9.85
12.83 12.08
Use the information in this table to answer the next 3 questions.
11. The “best” value of s in the table corresponds to the model with how many predictors?
a) 2 predictors
b) 3 predictors
c) 4 predictors
d) 5 predictors
e) 6 predictors
12. Generally speaking, the values of PRESS in the table are
a) encouraging because they are not too different from the corresponding values of SSE
b) discouraging because they are not too different from the corresponding values of SSE
c) encouraging because they are all larger than the corresponding numbers of predictors
d) discouraging because they are all larger than the corresponding numbers of predictors
13. The values of C p in the table suggest that
a)
b)
c)
d)
e)
any of the models could be used to effectively describe costlog
at least 2 predictors should be used in modeling costlog
at least 3 predictors should be used in modeling costlog
at least 4 predictors should be used in modeling costlog
at least 5 predictors should be used in modeling costlog
JMP MLR reports for the models indicated above with 2,3,4, and 7 predictors are available to you.
Use them in answering the following questions about multiple linear regression analyses of the data.
4
14. In the model with 3 predictors ( sizelog , indcost , ( indcost ) ) I am interested in testing
2
H 0 :β sizelog = βindcost = β indcost 2 = 0 . An F value for this overall model utility test is
(
a)
b)
c)
d)
e)
)
8.03
15.13
29.94
48.37
58.16
15. After accounting for the 3 predictors ( sizelog , indcost , ( indcost ) ), does the 4th ( central ) provide
2
statistically detectable additional explanatory power regarding the response ( costlog )?
a) Yes. The p -value for testing H 0 :β central = 0 in the 4-predictor model is less than .1.
b) No. The p -value for testing H 0 :β central = 0 in the 4-predictor model is less than .1.
c) Yes. The p -value for testing H 0 :β central = 0 in the 4-predictor model is larger than .1.
d) No. The p -value for testing H 0 :β central = 0 in the 4-predictor model is larger than .1.
e) Not enough information is given to find a relevant p -value .
16. There is an F statistic useful for comparing the 3-predictor model to the 7-predictor model.
Degrees of freedom for that statistic are
a) 3 and 7
b) 4 and 65
c) 3 and 65
d) 4 and 69
e) 3 and 69
17. The numerator sum of squares for the F statistic referred to in question 16 is
a) 11.87
b) 11.49
c)
.38
d)
.18
e) not computable based on the information provided on the JMP reports provided here
18. There is an F statistic for testing H 0 :β sizelog = βindcost = β indcost 2 = 0 in the 7-predictor model. The
(
)
numerator sum of squares for that statistic is
a) 11.87
b) 11.49
c)
.38
d)
.18
e) not computable based on the information provided on the JMP reports provided here
Henceforth suppose that one has settled on the model with 3 predictors ( sizelog , indcost , ( indcost ) ).
2
The rest of the questions in this exam refer to analyses based on this model.
5
19. In the model with the 3 predictors ( sizelog , indcost , ( indcost ) ), what do you estimate to be the
2
standard deviation of costlog for any fixed combination of sizelog and indcost (and therefore
( indcost )
a)
b)
c)
d)
e)
2
)?
.044
.358
.550
.566
.700
20. The lower and upper 2.5% points of the χ 2 distribution with 69 degrees of freedom are
respectively 47.92 and 93.86. 95% confidence limits for the standard deviation referred to in question
19 can then be obtained by multiplying the answer to 19 by
a) 47.92 and 93.86
1
1
b)
and
93.86
47.92
69
69
and
c)
93.86
47.92
69
69
d)
and
93.86
47.92
e) None of a)-d) is correct
21. According to 95% confidence limits based on the model with 3 predictors, if one increases
2
sizelog by .1 unit while holding indcost (and therefore ( indcost ) ) constant, average costlog should
increase by how much?
a) −.034 ± .009
b) −.034 ± .034
c) −.34 ± .09
d) −.34 ± .34
e) 2.76 − .034 + 2.72 indcost − 1.56 ( indcost ) ± 2.00 ( SE µˆ )
2
22. According to the fitted 3-predictor model, two firms with the same sizelog but respective indcost
values of .1 and .5 have predicted costlog values that differ by approximately
a) .4(2.72) = 1.09
b) 2.72(.4) − 1.56(.4) 2 = .84
c)
( 2.72 (.5) − 1.56 (.5) ) − ( 2.72 (.1) − 1.56 (.1) ) = .71
2
2
d) None of a)-c) are correct, as the answer depends on the value of sizelog
On the next page is a part of the JMP data table with some columns added based on the fitting of the 3predictor model. You may use it in addition to the JMP reports in answering the last few questions.
6
23. 95% prediction limits for the value of costlog for a company not represented in the data set that
has sizelog = 9.55 and indcost = .32 are
a) .27 ± 2.00(.07)
b) .27 ± 2.00 (.36 )
c) .27 ± 2.00 (.36 ) 74 / 73
d) .27 ± 2.00 (.43)
e) .27 ± 2.00
(.36 ) + (.07 )
2
2
24. Company 16 has the largest value of “h COSTLOG” in the part of the data table shown above (and
indeed in the whole table). In retrospect, this is sensible because
a) because case 16 has a large residual
b) because case 16 has a small residual
c) because case 16 has a large predicted value
d) because case 16 has a very small value of sizelog and a very large value of indcost
25. Case 15 has the largest residual in the part of the data table shown above. (In fact, no other
residual for the entire data set is larger in magnitude than .78.) If that case were to be dropped from
the data set and the 3-predictor model refit, one would expect
a) R 2 to decrease and s to decrease
b) R 2 to increase and s to decrease
c) R 2 to decrease and s to increase
d) R 2 to increase and s to increase
7
328 Final 04 Data
Rows FIRMCOST
COSTLOG
ASSUME
CAP
SIZELOG
INDCOST
INDCOST-SQUARED
CENTRAL
SOPH
3.29
9.31
4.07
6.94
5.35
28.86
2.79
15
3.89
4.07
4.34
4.33
5.29
7.9
97.55
65
8.51
4.31
12.45
2.55
8.18
11.29
1.25
11.92
0.65
3.15
19.38
3.75
13.33
4.58
13.96
0.28
6.08
0.94
2.97
4.11
1.22
6.29
6.12
3.51
2.16
0.36
7.83
5.09
0.2
8.85
0.76
5.71
17.53
14
2.06
0.93
10
5.82
9.13
9
12.61
2.15
22.22
12.71
15.97
4.32
8.49
5.25
18.33
21.72
0.4
3.7
15
18
29.12
79.3
13.57
0.5171959
0.96894968
0.60959441
0.84135947
0.72835378
1.46029633
0.4456042
1.17609126
0.5899496
0.60959441
0.63748973
0.6364879
0.72345567
0.89762709
1.98922727
1.81291336
0.92992956
0.63447727
1.09516935
0.40654018
0.9127533
1.05269394
0.09691001
1.07627626
-0.1870866
0.49831055
1.28735377
0.57403127
1.12483015
0.66086548
1.14488542
-0.552842
0.78390358
-0.0268721
0.47275645
0.61384182
0.08635983
0.79865065
0.78675142
0.54530712
0.33445375
-0.4436975
0.89376176
0.70671778
-0.69897
0.94694327
-0.1191864
0.75663611
1.24378192
1.14612804
0.31386722
-0.0315171
1
0.76492298
0.96047078
0.95424251
1.10071509
0.33243846
1.34674405
1.10414555
1.20330492
0.63548375
0.92890769
0.7201593
1.26316246
1.33685982
-0.39794
0.56820172
1.17609126
1.25527251
1.46419137
1.89927319
1.13257985
0.29
0.89
1.67
1.21
0.28
14.86
0.85
1.47
3.47
5.86
0.39
2.08
1.14
0.24
0.18
1.27
0.23
0.5
1.02
0.44
3.86
2.98
0.01
1.68
0.09
0.21
0.34
3.28
0.83
0.44
0.02
0
0.5
0.01
0.17
0.17
0.5
0.01
0.05
0.33
0.9
0.07
1.67
0.5
0.07
1.35
0.02
1.53
0.13
0.63
0.33
0.79
0.71
0.29
2.5
2.03
61.82
0.13
0.42
3.42
0.79
1.9
0.29
6.46
0.29
0.92
0
0.43
2.92
2.3
0.79
0.51
37.14
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
9.55
8.04
7.9
8.1
7.74
8.16
9.47
8.13
7.5
8.55
8.08
8.01
7.59
8.52
9.31
6.68
8.39
8.86
8.3
10.12
7
7.65
8.52
6.29
8.7
8.59
7.38
8.07
8.01
8.48
8.49
9.86
7.6
8.16
7.45
8.41
10.6
9.04
8.26
9.15
8.96
9.95
8.01
7
10.27
8.27
10.02
8.16
7.31
8.99
9.1
9.55
8.16
8.55
8.29
7.6
7.42
9.01
7.5
7.09
8.95
8.58
8.58
8.29
8.7
7.5
10.36
8.17
7.5
9.21
7.96
5.27
7.24
0.32
0.33
0.34
0.34
0.09
0.42
0.41
0.32
0.53
1.22
0.26
0.34
0.42
0.33
0.62
1.22
0.63
0.42
0.32
0.34
0.42
0.34
0.41
0.34
0.1
0.5
0.33
0.33
0.53
0.34
0.5
0.1
0.33
0.33
0.1
0.33
0.34
0.86
0.33
0.32
0.34
0.34
0.26
0.33
0.1
0.33
0.5
0.26
0.86
0.33
0.33
0.34
0.5
0.5
0.32
0.5
0.62
0.32
0.33
0.32
0.62
0.32
0.32
0.42
0.86
0.41
0.41
0.34
0.34
0.86
0.33
0.32
0.86
0.1024
0.1089
0.1156
0.1156
0.0081
0.1764
0.1681
0.1024
0.2809
1.4884
0.0676
0.1156
0.1764
0.1089
0.3844
1.4884
0.3969
0.1764
0.1024
0.1156
0.1764
0.1156
0.1681
0.1156
0.01
0.25
0.1089
0.1089
0.2809
0.1156
0.25
0.01
0.1089
0.1089
0.01
0.1089
0.1156
0.7396
0.1089
0.1024
0.1156
0.1156
0.0676
0.1089
0.01
0.1089
0.25
0.0676
0.7396
0.1089
0.1089
0.1156
0.25
0.25
0.1024
0.25
0.3844
0.1024
0.1089
0.1024
0.3844
0.1024
0.1024
0.1764
0.7396
0.1681
0.1681
0.1156
0.1156
0.7396
0.1089
0.1024
0.7396
1
2
2
1
3
3
1
1
2
1
5
4
3
2
2
2
2
1
1
1
3
1
5
1
2
2
1
2
2
3
3
1
3
1
3
4
1
2
4
1
2
4
2
4
1
1
3
3
1
4
1
2
1
2
5
4
1
4
1
2
3
3
1
1
1
4
5
1
1
3
1
4
3
25
24
15
16
18
25
11
22
18
27
26
11
20
22
17
26
23
19
11
17
30
24
24
25
23
19
27
23
18
18
29
5
22
18
25
25
13
20
23
27
19
22
25
26
25
24
19
24
18
23
24
28
27
9
31
24
24
23
18
27
28
27
15
11
25
18
21
17
14
18
19
23
20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
Multivariate
Correlations
COSTLOG
1.0000
0.1645
-0.0881
-0.6366
0.3946
-0.0544
0.1441
COSTLOG
ASSUME
CAP
SIZELOG
INDCOST
CENTRAL
SOPH
ASSUME
0.1645
1.0000
0.2310
-0.2092
0.2493
-0.0681
0.0618
CAP
-0.0881
0.2310
1.0000
0.1962
0.1225
-0.0038
-0.0866
SIZELOG
-0.6366
-0.2092
0.1962
1.0000
-0.1022
-0.0798
-0.2089
INDCOST
0.3946
0.2493
0.1225
-0.1022
1.0000
-0.0849
0.0927
CENTRAL
-0.0544
-0.0681
-0.0038
-0.0798
-0.0849
1.0000
0.2826
SOPH
0.1441
0.0618
-0.0866
-0.2089
0.0927
0.2826
1.0000
Bivariate Fit of COSTLOG By SIZELOG
2.5
2
COSTLOG
1.5
1
0.5
0
-0.5
-1
4
5
6
7
8
9
10
11
12
SIZELOG
Linear Fit
Linear Fit
COSTLOG = 3.6813956 - 0.3509918 SIZELOG
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.405227
0.39685
0.412531
0.756961
73
Analysis of Variance
Source
Model
Error
C. Total
DF
1
71
72
Sum of Squares
8.232268
12.082913
20.315181
Mean Square
8.23227
0.17018
F Ratio
48.3734
Prob > F
<.0001
Parameter Estimates
Term
Intercept
SIZELOG
Estimate
3.6813956
-0.350992
Std Error
0.423237
0.050465
t Ratio
8.70
-6.96
Prob>|t|
<.0001
<.0001
1
Response COSTLOG
Whole Model
Actual by Predicted Plot
COSTLOG Actual
2
1.5
1
0.5
0
-0.5
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted P<.0001 RSq=0.52
RMSE=0.3752
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.515
0.501143
0.375174
0.756961
73
Analysis of Variance
Source
Model
Error
C. Total
DF
2
70
72
Sum of Squares
10.462318
9.852863
20.315181
Mean Square
5.23116
0.14076
F Ratio
37.1649
Prob > F
<.0001
Parameter Estimates
Term
Intercept
SIZELOG
INDCOST
Estimate
3.1827934
-0.332229
0.8181391
Std Error
0.40478
0.046137
0.205543
t Ratio
7.86
-7.20
3.98
Prob>|t|
<.0001
<.0001
0.0002
Effect Tests
Source
SIZELOG
INDCOST
Nparm
1
1
DF
1
1
Sum of Squares
7.2986719
2.2300505
F Ratio
51.8537
15.8435
Prob > F
<.0001
0.0002
Residual by Predicted Plot
COSTLOG Residual
1.5
1.0
0.5
0.0
-0.5
-1.0
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted
2
Response COSTLOG
Whole Model
Actual by Predicted Plot
COSTLOG Actual
2
1.5
1
0.5
0
-0.5
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted P<.0001 RSq=0.57
RMSE=0.3577
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.565539
0.54665
0.357652
0.756961
73
Analysis of Variance
Source
Model
Error
C. Total
DF
3
69
72
Sum of Squares
11.489035
8.826146
20.315181
Mean Square
3.82968
0.12792
F Ratio
29.9392
Prob > F
<.0001
Parameter Estimates
Term
Intercept
SIZELOG
INDCOST
INDCOST-SQUARED
Estimate
2.758867
-0.335531
2.7202067
-1.55693
Std Error
0.413872
0.043998
0.699379
0.549547
t Ratio
6.67
-7.63
3.89
-2.83
Prob>|t|
<.0001
<.0001
0.0002
0.0060
Effect Tests
Source
SIZELOG
INDCOST
INDCOST-SQUARED
Nparm
1
1
1
DF
1
1
1
Sum of Squares
7.4392512
1.9350882
1.0267169
F Ratio
58.1577
15.1279
8.0265
Prob > F
<.0001
0.0002
0.0060
Residual by Predicted Plot
COSTLOG Residual
1.5
1.0
0.5
0.0
-0.5
-1.0
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted
3
Response COSTLOG
Whole Model
Actual by Predicted Plot
COSTLOG Actual
2
1.5
1
0.5
0
-0.5
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted P<.0001 RSq=0.58
RMSE=0.3563
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.575048
0.550051
0.356308
0.756961
73
Analysis of Variance
Source
Model
Error
C. Total
DF
4
68
72
Sum of Squares
11.682210
8.632971
20.315181
Mean Square
2.92055
0.12696
F Ratio
23.0045
Prob > F
<.0001
Parameter Estimates
Term
Intercept
SIZELOG
INDCOST
INDCOST-SQUARED
CENTRAL
Estimate
2.8845308
-0.340543
2.7794187
-1.624071
-0.041764
Std Error
0.424716
0.04402
0.698402
0.55018
0.033858
t Ratio
6.79
-7.74
3.98
-2.95
-1.23
Prob>|t|
<.0001
<.0001
0.0002
0.0043
0.2216
Effect Tests
Source
SIZELOG
INDCOST
INDCOST-SQUARED
CENTRAL
Nparm
1
1
1
1
DF
1
1
1
1
Sum of Squares
7.5978749
2.0107054
1.1062449
0.1931749
F Ratio
59.8468
15.8379
8.7136
1.5216
Prob > F
<.0001
0.0002
0.0043
0.2216
Residual by Predicted Plot
COSTLOG Residual
1.5
1.0
0.5
0.0
-0.5
-1.0
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted
4
Response COSTLOG
Whole Model
Actual by Predicted Plot
COSTLOG Actual
2
1.5
1
0.5
0
-0.5
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted P<.0001 RSq=0.58
RMSE=0.3605
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.584112
0.539325
0.36053
0.756961
73
Analysis of Variance
Source
Model
Error
C. Total
DF
7
65
72
Sum of Squares
11.866351
8.448830
20.315181
Mean Square
1.69519
0.12998
F Ratio
13.0418
Prob > F
<.0001
Parameter Estimates
Term
Intercept
SIZELOG
INDCOST
INDCOST-SQUARED
CENTRAL
ASSUME
SOPH
CAP
Estimate
2.8298768
-0.347015
2.9689726
-1.745744
-0.050031
-0.005957
0.004215
0.0022153
Std Error
0.498185
0.047654
0.725151
0.566816
0.036039
0.005556
0.00865
0.095313
t Ratio
5.68
-7.28
4.09
-3.08
-1.39
-1.07
0.49
0.02
Prob>|t|
<.0001
<.0001
0.0001
0.0030
0.1698
0.2876
0.6277
0.9815
Effect Tests
Source
SIZELOG
INDCOST
INDCOST-SQUARED
CENTRAL
ASSUME
SOPH
CAP
Nparm
1
1
1
1
1
1
1
DF
1
1
1
1
1
1
1
Sum of Squares
6.8924962
2.1789051
1.2329913
0.2504999
0.1494455
0.0308669
0.0000702
F Ratio
53.0265
16.7631
9.4859
1.9272
1.1497
0.2375
0.0005
Prob > F
<.0001
0.0001
0.0030
0.1698
0.2876
0.6277
0.9815
Residual by Predicted Plot
COSTLOG Residual
1.5
1.0
0.5
0.0
-0.5
-1.0
-0.5
.0
.5
1.0
1.5
2.0
COSTLOG Predicted
5