252y0581s 12/5/05
ECO252 QBA2
Final EXAM
May 2-6, 2005
TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
Class days and time : _________________________
III Take-home Exam (20+ points)
A) 4th computer problem (5+)
This is an internet project. You should do only one of the following 2 problems.
Problem 1: In his book, Statistics for Economists: An Intuitive Approach (New York, HarperCollins,
1992), Alan S. Caniglia presents data for 50 states and the District of Columbia. These data are presented as
an appendix at the end of this section.
The Data Consists of six variables.
The dependent variable, MIM, the mean income of males (having income) who are 18 years of age or older.
PMHS, the percent of males 18 and older who are high school graduates.
PURBAN, the percent of total population living in an urban area.
MAGE, the median age of males.
Using his data, I got the results below.
Regression Analysis: MIM versus PMHS
The regression equation is
MIM = 2736 + 180 PMHS
Predictor
Constant
PMHS
Coef
2736
180.08
S = 1430.91
SE Coef
2174
31.31
R-Sq = 40.3%
T
1.26
5.75
P
0.214
0.000
R-Sq(adj) = 39.1%
Analysis of Variance
Source
DF
SS
Regression
1
67720854
Residual Error 49 100328329
Total
50 168049183
MS
67720854
2047517
F
33.07
P
0.000
Unusual Observations
Obs PMHS
MIM
Fit SE Fit Residual St Resid
1 69.1 12112 15180
200
-3068
-2.17R
3 71.6 12711 15630
215
-2919
-2.06R
50 81.9 21552 17485
447
4067
2.99R
R denotes an observation with a large standardized residual.
His only comment is that a 1% increase in the percent of males that are college graduates results is
associated with about a $180 increase in male income and that there is evidence her that the relationship is
significant.
He then describes three dummy variables: NE = 1 if the state is in the Northeast (Maine through
Pennsylvania in his listing); MW = 1 if the state is in the Midwest (Ohio through Kansas) and SO = 1 if the
state is in the South (Delaware through Texas). If all of the dummy variables are zero, the state is in the
West (Montana through Hawaii). I ran the regression with all six independent variables.
MTB > regress c2 6 c3-c8;
SUBC> VIF;
SUBC> brief 2.
Regression Analysis: MIM versus PMHS, PURBAN, MAGE, NE, MW, SO
The regression equation is
MIM = - 1294 + 198 PMHS + 49.4 PURBAN - 42 MAGE + 247 NE + 757 MW + 1269 SO
252y0581s 12/5/05
Predictor
Constant
PMHS
PURBAN
MAGE
NE
MW
SO
Coef
-1294
198.13
49.36
-42.1
246.6
756.7
1268.9
S = 1271.71
SE Coef
5394
53.97
14.27
151.6
723.7
608.2
863.0
R-Sq = 57.7%
T
-0.24
3.67
3.46
-0.28
0.34
1.24
1.47
DF
1
1
1
1
1
1
VIF
3.8
1.4
1.5
2.4
2.1
5.2
R-Sq(adj) = 51.9%
Analysis of Variance
Source
DF
SS
Regression
6
96890414
Residual Error 44
71158768
Total
50 168049183
Source
PMHS
PURBAN
MAGE
NE
MW
SO
P
0.811
0.001
0.001
0.783
0.735
0.220
0.149
MS
16148402
1617245
F
9.99
P
0.000
Seq SS
67720854
23781889
281110
1416569
193443
3496549
Unusual Observations
Obs PMHS
MIM
Fit SE Fit Residual St Resid
50 81.9 21552 16999
543
4553
3.96R
R denotes an observation with a large standardized residual.
He has asked whether region affects the independent variable, on the strength of the significance tests in the
output above, he concludes that the regional variables do not have any affect on male income. (Median Age
looks pretty bad too.)
There are two ways to confirm these conclusions. Caniglia does one of these, an F test that shows whether
the regional variables as a group have any effect. He says that they do not. Another way to test this is by
using a stepwise regression.
MTB > stepwise c2 c3-c8
Stepwise Regression: MIM versus PMHS, PURBAN, MAGE, NE, MW, SO
Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15
Response is MIM on 6 predictors, with N = 51
Step
Constant
1
2736
2
2528
PMHS
T-Value
P-Value
180
5.75
0.000
134
4.46
0.000
PURBAN
T-Value
P-Value
S
R-Sq
R-Sq(adj)
Mallows C-p
50
3.86
0.000
1431
40.30
39.08
15.0
1263
54.45
52.55
2.3
More? (Yes, No, Subcommand, or Help)
SUBC> y
No variables entered or removed
More? (Yes, No, Subcommand, or Help)
SUBC> n
What happens is that the computer picks PMHS as the most valuable independent variable, and gets the
same result that appeared in the simple regression above. It then adds PURBAN and gets
MIM = 2528 + 134 PMHS + 50 PURBAN. The coefficients of the 2 independent variables are significant, the
adjusted R-Sq is higher than the adjusted R-sq with all 6 predictors and the computer refuses to add any
more independent variables. So it looks like we have found our ‘best’ regression. (See the text for
interpretation VIFs and C-p’s.)
252y0581s 12/5/05
So here is your job. Update this work. Use any income per person variable, a mean or a median for men,
women or everybody. Find measures of urbanization or median age. Fix the categorization of states if you
don’t like it. Regress state incomes against the revised data. Remove the variables with insignificant
coefficients. If you can think of new variables add them. (Last year I suggested trying percent of output or
labor force in manufacturing.) Make sure that you pick variables that can be compared state to state.
Though you can legitimately ask whether size of a state affects per capita income, using total amount
produced in manufacturing is poor because it’s just going to be big for big states. Similarly the fraction of
the workforce with a certain education level is far better then the number. For instructions on how to do a
regression, try the material in Doing a Regression. For data sources, try the sites mentioned in 252datalinks.
Problem 2: Recently the Heritage Foundation produced the graph below.
What I want to know is if you can develop an equation relating per capita income (the dependent variable)
and Economic freedom x  . Because it is pretty obvious that a straight line won’t work, you will probably
need to create a x 2 variable too. But I would like to know what parts of ‘economic freedom’ affect per
capita income. In addition to the Heritage Foundation Sources, the CIFP site mentioned in 252datalinks,
and the CIA Factbook might provide some interesting independent variables. You should probably use a
sample of no more than 50 countries and it’s up to you what variables to use. You are, of course, looking
for significant coefficients and high R-squares. For instructions on how to do a regression, try the material
in Doing a Regression.
252y0581s 12/5/05
B. Do only Problem 1 or problem 2. (Problem Due to Donald R Byrkit). Four different job candidates are
interviewed by seven executives. These are rated for 7 traits on a scale of 1-10 and the scores are added
together to create a total score for each candidate-rater pair that is between 0 and 70. The results appear
below.
Row
1
2
3
4
5
6
7
Sum
Sum
Sum
Sum
Sum
Sum
Raters
Moore
Gaston
Heinrich
Seldon
Greasy
Waters
Pierce
of
of
of
of
of
of
Lee
52
38
54
43
58
36
52
Candidates
Jacobs
25
31
38
30
44
28
41
Wilkes
29
24
40
31
46
22
37
Delap
33
29
39
28
47
25
45
Jacobs = 237
squares (uncorrected) of Jacobs = 8331
Wilkes = 229
squares (uncorrected) of Wilkes = 7947
Delap = 246
squares (uncorrected) of Delap = 9094
Personalize the data by adding the second to last digit of of your student number to Lee’s column. For
example Roland Dough’s student number is 123689, so he uses 52 + 8 = 60, 38 + 8 = 46, 62 etc. If the
second to last digit of your student number is zero, add 10.
Problem 1: a) Assume that a Normal distribution applies and use a statistical prodedure to compare the
column means, treating each column as an independent random sample. If you conclude that there is a
difference between the column means, use an individual confidence interval to see if there is a significant
difference between the best and second-best candidate. If you conclude that there is no difference between
the means, use an individual confidence interval to see if there is a significant difference between the best
and worst candidate. (6)
b) Now assume that a Normal distribution does not apply but that the columns are still independent randon
samples and use an appropriate procedure to compare the column medians. (4)
[16]
Problem 2: a) Assume that a Normal distribution applies and use a statistical prodedure to compare the
column means, taking note of the fact that each row represents one executive. If you conclude that there is a
difference between the column means, use an individual confidence interval to see if there is a significant
difference between the best and second-best candidate. If you conclude that there is no difference between
the column means, use an individual confidence interval to see if there is a significant difference between
the kindest and least kind executive. (8)
b) Now assume that a Normal distribution does not apply but that each row represents the opinion of one
rater and use an appropriate procedure to compare the column medians. (4)
c) Use Kendall’s coefficient of concordance to show how the raters differ and do a significance test. (3)
Problem 3: (Extra Credit) Decide between the methods used in Problem 1 and Problem 2. To do this test
for equal variances and for Normality on the computer. What is your decision? Why?
(4)
You can do most of this with the following commands in Minitab if you put your data in 3 columns of
Minitab with A, B, C and D above them.
MTB >
MTB >
SUBC>
SUBC>
MTB >
MTB >
AOVOneway A B C D
stack A B C D C11;
subscripts C12;
UseNames.
rank C11 C13
vartest C11 C12
MTB > Unstack (c13);
SUBC>
Subscripts c12;
SUBC>
After;
SUBC>
VarNames.
MTB > NormTest 'A';
SUBC>
KSTest.
#Does a 1-way ANOVA
# Stacks the data in c12, col.no. in c12.
#Puts the ranks of the stacked data in c13
#Does a bunch of tests, including Levene’s
On stacked data in c11 with IDs in c12.
#Unstacks the ranks in the next available
# columns. Uses IDs in c12.
#Does a test (apparently Lilliefors)for Normality
# on column A.
252y0581s 12/5/05
C. You may do both problems. These are intended to be done by hand. A table version of the data for
problem 2 is provided in 2005data1 which can be downloaded to Minitab. I do not want Minitab results for
these data except for Problem 2e.
Problem 1: Using data from the 1970s and 1980s, Alan S. Caniglia calculated a regression of
nonresidential investment on the change in level of final sales to verify the accelerator model of investment.
This theory says that because capital stock must be approximately proportional to production, investment
will be driven by changes in output. In order to check his work I put together a data set 2005series. The last
two years of the series are in Exhibit C1 below.
Exhibit C1
Row Date
73 1988 01
74 1988 02
75 1988 03
76 1988 04
77 1989 01
78 1989 02
79 1989 03
80 1989 04
RPFI
862.406
879.330
882.704
891.502
900.401
901.643
917.375
902.298
Sales
6637.22
6716.38
6749.47
6835.07
6873.33
6933.55
7015.34
7026.76
Sales-4Q
6344.41
6431.37
6510.82
6542.55
6637.22
6716.38
6749.47
6835.07
Change
292.815
285.006
238.644
292.522
236.106
217.171
265.876
191.695
DEFL %Y
2.897
3.318
3.699
3.724
4.013
4.016
3.596
3.537
MINT %
9.88
9.67
9.96
9.51
9.62
9.79
8.93
8.92
RINT
6.983
6.352
6.261
5.786
5.607
5.774
5.334
5.383
‘Date’ consists of the year and the quarter. ‘RPFI’ consists of real fixed private investment from
2005InvestSeries1. ‘Sales’ consists of sales data (actually a version of gross domestic product) from
2005SalesSeries1. ‘Sales-4Q’ (Sales 4 Quarters earlier’ is also sales data from 2005SalesSeries1, but is the
data of one year earlier. (Note that the 1989 numbers in ‘Sales-4Q’ are identical to the 1988 numbers in
‘Sales.’ ‘Change’ is ‘Sales’ – ‘Sales-4Q. ‘DEFL %Y’ is the percent change in the gross domestic deflator
over the last year (a measure of inflation) taken from 2005deflSeries1. ‘MINT %’ is an estimate of the
percent return on Aaa bonds taken from 2005intSeries1. Only the values for January, April, July and
October are used since quarterly data was not available. ‘RINT’ (an estimate of the real interest rate) is
‘MINT %’ - ‘DEFL %Y’.
These are manipulated in the input to the regression program as in Exhibit C2 below.
Exhibit C2
Row Time
73 1988 01
74 1988 02
75 1988 03
76 1988 04
77 1989 01
78 1989 02
79 1989 03
80 1989 04
Y
86.2406
87.9330
88.2704
89.1502
90.0401
90.1643
91.7375
90.2298
X1
29.2815
28.5006
23.8644
29.2522
23.6106
21.7171
26.5876
19.1695
X2
6.98
6.35
6.26
5.79
5.61
5.77
5.33
5.38
Here Y is ‘RFPI’ divided by 10. X1 is ‘Change’ divided by 10. X2 is ‘RINT’ rounded to eliminate the last
decimal place. If you don’t understand how I got Exhibit C2 from Exhibit C1 find out before you go
any further,
Personalize the data by adding one year (four values) to the data in 2005 series. Pick the year to be added
by adding the last digit of your student number to 1990. Make sure that I know the year you are using. Then
get, for your year, ‘RPFI’ from 2005InvestSeries1, ‘Sales’ from 2005SalesSeries1, ‘Sales-4Q’ from
2005SalesSeries1 (Make sure that you use the sales of one year earlier, not 1989 unless your year is 1990.),
‘DEFL %Y’ 2005deflSeries1 and ‘MINT %’ from 2005intSeries1. Calculate ‘Change’ by subtracting
‘Sales-4Q ’ from ‘Sales.’ If you are going to do Problem 2, calculate ‘RINT’ by subtracting ‘DEFL %Y’
from ‘MINT %.’ Present your four rows of new values in the format of Exhibit C1. Now manipulate your
numbers to the form in Exhibit C2 and again present your four rows of numbers. These are observations 81
through 84.
Now it’s time to compute your spare parts. The following are computed for you from the data for 1970
through 1989.
252y0581s 12/5/05
Sum of Y = 5323.20
Sum of X1 = 1283.42
Sum of X2 = 328.33
Sum of Ysq = 371032
Sum of X1sq = 30307.57
Sum of X2sq = 2080.65
Sum of X1Y = 92676.9
Sum of X2Y = 24188.2
Sum of X1X2 = 6324.09
 Y  5323 .2
 X 1  1283.42
 X 2  328.33
 Y  371032
 X  30307 .6
 X  2080 .65
 X 1 Y  92676.9
 X 2 Y 24188.2
 X 1 X 2  6324.09
n  80
2
2
1
2
2
Add the results of your data to these sums (You only need the sums involving X1 and Y if you are not doing
Problem 2.) (Show your work!) and do the following.
a. Compute the regression equation Yˆ  b0  b1 x1 to predict investment on the basis of change in
sales only. (2)
b. Compute R 2 . (2)
c. Compute s e . (2)
d. Compute s b0 and do a significance test on b0 (1.5)
e. Compute s b1 and do a significance test on b1 (2)
f. In the first quarter of 2001 sales were 9883.167, the interest rate was 7.15% and the gdp inflation
rate was 2.176%. In the first quarter of 2000 sales were 9668.827. Get values of Y and X1 from
this and predict the level of investment for 2001. Using this create a confidence interval or a
prediction interval for investment in 2001 as appropriate. (3)
g. Do an ANOVA table for the regression. What conclusion can you draw from the hypothesis test
in the ANOVA? (2)
[30]
Problem 2: Continue with the data in problem 1.
a. Compute the regression equation Yˆ  b0  b1 x1  b2 x 2 to predict investment on the basis of real
interest rates and change in sales. Do not attempt to use the value of b1 you got in problem 1. Is
the sign of the coefficient what you expected? Why? (5)
b. Compute R-squared and R-squared adjusted for degrees of freedom for this regression and
compare them with the values for the previous problem. (2)
c. Using either R – squares or SST, SSR and SSE do an F tests (ANOVA). First check the
usefulness of the multiple regression and show whether the use of real interest rates gives a
significant improvement in explanatory power of the regression? (Don’t say a word without
referring to a statistical test.) (3)
d. Use the values in 1f to compute a predicition for 2001 investment. By what percent does the
predicted investment change if you add real interest rates. (2)
e. If you are prepared to explain the results of VIF and Durbin-Watson (Check the text!), run the
regression of Y on X1 and X2 using
MTB > Regress Y 2 X1 X2;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
Explain your results. (2)
[44]
252y0581s 12/5/05
————— 12/5/2005 6:36:00 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x050812B.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x05081-2B.MTW'
Worksheet was saved on Fri Dec 02 2005
Results for: 252x05081-2B.MTW
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x050812B.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x05081-2B.MTW'
Existing file replaced.
MTB > Print c11-c18
Data Display
Row
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
Date
1970
1970
1970
1970
1971
1971
1971
1971
1972
1972
1972
1972
1973
1973
1973
1973
1974
1974
1974
1974
1975
1975
1975
1975
1976
1976
1976
1976
1977
1977
1977
1977
1978
1978
1978
1978
1979
1979
1979
1979
1980
1980
1980
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
RPFI
438.783
429.062
436.651
436.970
446.842
465.210
474.075
487.205
508.931
517.997
523.622
547.866
571.154
576.056
574.361
568.585
555.187
547.212
537.591
507.168
476.057
469.408
481.178
490.126
510.526
519.190
524.579
551.527
571.473
603.340
611.248
622.480
627.551
673.168
692.409
707.033
712.607
706.983
719.777
713.078
702.987
641.822
648.101
Sales
3777.99
3770.96
3804.63
3797.22
3844.65
3871.30
3905.17
3952.51
4006.87
4073.05
4109.55
4204.81
4296.37
4317.35
4322.62
4327.31
4322.72
4328.67
4316.28
4254.50
4287.78
4331.02
4370.06
4421.11
4482.11
4496.26
4523.69
4587.13
4631.54
4705.53
4755.21
4794.05
4799.52
4989.95
5036.02
5100.63
5117.81
5117.91
5192.28
5216.88
5227.32
5126.20
5193.45
Sales-4Q
3730.46
3748.61
3767.64
3768.13
3777.99
3770.96
3804.63
3797.22
3844.65
3871.30
3905.17
3952.51
4006.87
4073.05
4109.55
4204.81
4296.37
4317.35
4322.62
4327.31
4322.72
4328.67
4316.28
4254.50
4287.78
4331.02
4370.06
4421.11
4482.11
4496.26
4523.69
4587.13
4631.54
4705.53
4755.21
4794.05
4799.52
4989.95
5036.02
5100.63
5117.81
5117.91
5192.28
Diff
47.533
22.352
36.992
29.086
66.664
100.337
100.533
155.290
162.219
201.749
204.385
252.308
289.496
244.305
213.071
122.494
26.353
11.322
-6.344
-72.813
-34.942
2.343
53.780
166.611
194.331
165.245
153.630
166.026
149.433
209.264
231.518
206.922
167.978
284.421
280.809
306.577
318.289
127.960
156.265
116.247
109.513
8.296
1.172
DEFL %Y
5.580
5.663
4.994
4.982
5.060
4.995
5.216
4.706
4.770
4.032
3.991
4.536
4.160
5.144
6.162
6.845
7.595
8.451
9.504
10.589
11.008
10.105
8.949
7.645
6.391
5.918
5.408
5.476
6.033
6.428
6.270
6.639
6.481
6.887
7.351
7.286
7.574
8.246
8.775
8.651
9.021
8.747
8.870
MINT %
7.91
7.83
8.44
8.03
7.36
7.25
7.64
7.39
7.19
7.30
7.21
7.21
7.15
7.26
7.45
7.60
7.83
8.25
8.72
9.27
8.83
8.95
8.84
8.86
8.60
8.40
8.56
8.32
7.96
8.04
7.94
8.04
8.41
8.56
8.88
8.89
9.25
9.38
9.20
10.13
11.09
12.04
11.07
RINT
2.330
2.167
3.446
3.048
2.300
2.255
2.424
2.684
2.420
3.268
3.219
2.674
2.990
2.116
1.288
0.755
0.235
-0.201
-0.784
-1.319
-2.178
-1.155
-0.109
1.215
2.209
2.482
3.152
2.844
1.927
1.612
1.670
1.401
1.929
1.673
1.529
1.604
1.676
1.134
0.425
1.479
2.069
3.293
2.200
252y0581s 12/5/05
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01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
673.823
678.726
683.209
683.276
680.824
659.955
637.003
619.256
618.199
631.832
656.160
695.331
735.996
759.065
790.361
807.335
821.942
828.138
838.581
831.815
847.563
848.806
846.758
841.956
847.480
830.807
845.666
863.665
863.631
862.406
879.330
882.704
891.502
900.401
901.643
917.375
902.298
5239.72
5261.68
5272.81
5278.47
5247.43
5232.89
5230.54
5196.58
5273.29
5329.22
5404.57
5505.11
5577.04
5614.42
5717.49
5770.20
5854.63
5953.01
5998.50
6095.81
6121.19
6184.14
6230.50
6317.76
6354.95
6344.41
6431.37
6510.82
6542.55
6637.22
6716.38
6749.47
6835.07
6873.33
6933.55
7015.34
7026.76
5216.88
5227.32
5126.20
5193.45
5239.72
5261.68
5272.81
5278.47
5247.43
5232.89
5230.54
5196.58
5273.29
5329.22
5404.57
5505.11
5577.04
5614.42
5717.49
5770.20
5854.63
5953.01
5998.50
6095.81
6121.19
6184.14
6230.50
6317.76
6354.95
6344.41
6431.37
6510.82
6542.55
6637.22
6716.38
6749.47
6835.07
MTB > print c1-c4
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Time
1970
1970
1970
1970
1971
1971
1971
1971
1972
1972
1972
1972
1973
1973
1973
1973
1974
1974
1974
1974
1975
1975
1975
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
Y
43.8783
42.9062
43.6651
43.6970
44.6842
46.5210
47.4075
48.7205
50.8931
51.7997
52.3622
54.7866
57.1154
57.6056
57.4361
56.8585
55.5187
54.7212
53.7591
50.7168
47.6057
46.9408
48.1178
X1
4.7533
2.2352
3.6992
2.9086
6.6664
10.0337
10.0533
15.5290
16.2219
20.1749
20.4385
25.2308
28.9496
24.4305
21.3071
12.2494
2.6353
1.1322
-0.6344
-7.2813
-3.4942
0.2343
5.3780
X2
2.33
2.17
3.45
3.05
2.30
2.26
2.42
2.68
2.42
3.27
3.22
2.67
2.99
2.12
1.29
0.76
0.24
-0.20
-0.78
-1.32
-2.18
-1.16
-0.11
22.839
34.356
146.602
85.014
7.711
-28.793
-42.262
-81.891
25.865
96.336
174.029
308.529
303.747
285.201
312.921
265.094
277.588
338.591
281.004
325.610
266.558
231.128
232.007
221.953
233.764
160.267
200.870
193.062
187.596
292.815
285.006
238.644
292.522
236.106
217.171
265.876
191.695
9.691
10.196
9.839
9.313
8.307
7.021
6.321
5.937
5.161
4.602
4.095
3.696
3.365
3.804
3.949
3.718
3.595
3.468
3.168
2.774
2.784
2.165
2.106
2.274
2.282
2.597
2.629
2.799
2.872
2.897
3.318
3.699
3.724
4.013
4.016
3.596
3.537
12.31
12.81
13.88
14.38
15.40
15.18
14.46
14.61
12.12
11.79
11.51
12.15
12.25
12.20
12.81
13.44
12.63
12.08
12.23
10.97
11.02
10.05
8.79
8.88
8.86
8.36
8.85
9.42
10.52
9.88
9.67
9.96
9.51
9.62
9.79
8.93
8.92
2.619
2.614
4.041
5.067
7.093
8.159
8.139
8.673
6.959
7.188
7.415
8.454
8.885
8.396
8.861
9.722
9.035
8.612
9.062
8.196
8.236
7.885
6.684
6.606
6.578
5.763
6.221
6.621
7.648
6.983
6.352
6.261
5.786
5.607
5.774
5.334
5.383
252y0581s 12/5/05
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
74
75
76
77
78
79
80
1975
1976
1976
1976
1976
1977
1977
1977
1977
1978
1978
1978
1978
1979
1979
1979
1979
1980
1980
1980
1980
1981
1981
1981
1981
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
1986
1986
1987
1987
1987
1987
1988
1988
1988
1988
1989
1989
1989
1989
MTB >
SUBC>
SUBC>
SUBC>
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
01
02
03
04
49.0126
51.0526
51.9190
52.4579
55.1527
57.1473
60.3340
61.1248
62.2480
62.7551
67.3168
69.2409
70.7033
71.2607
70.6983
71.9777
71.3078
70.2987
64.1822
64.8101
67.3823
67.8726
68.3209
68.3276
68.0824
65.9955
63.7003
61.9256
61.8199
63.1832
65.6160
69.5331
73.5996
75.9065
79.0361
80.7335
82.1942
82.8138
83.8581
83.1815
84.7563
84.8806
84.6758
84.1956
84.7480
83.0807
84.5666
86.3665
86.3631
86.2406
87.9330
88.2704
89.1502
90.0401
90.1643
91.7375
90.2298
16.6611
19.4331
16.5245
15.3630
16.6026
14.9433
20.9264
23.1518
20.6922
16.7978
28.4421
28.0809
30.6577
31.8289
12.7960
15.6265
11.6247
10.9513
0.8296
0.1172
2.2839
3.4356
14.6602
8.5014
0.7711
-2.8793
-4.2262
-8.1891
2.5865
9.6336
17.4029
30.8529
30.3747
28.5201
31.2921
26.5094
27.7588
33.8591
28.1004
32.5610
26.6558
23.1128
23.2007
22.1953
23.3764
16.0267
20.0870
19.3062
18.7596
29.2815
28.5006
23.8644
29.2522
23.6106
21.7171
26.5876
19.1695
regress c2 1 c3;
VIF;
DW;
Brief 2.
Regression Analysis: Y versus X1
The regression equation is
Y = 54.5 + 0.749 X1
1.22
2.21
2.48
3.15
2.84
1.93
1.61
1.67
1.40
1.93
1.67
1.53
1.60
1.68
1.13
0.43
1.48
2.07
3.29
2.20
2.62
2.61
4.04
5.07
7.09
8.16
8.14
8.67
6.96
7.19
7.42
8.45
8.89
8.40
8.86
9.72
9.04
8.61
9.06
8.20
8.24
7.89
6.68
6.61
6.58
5.76
6.22
6.62
7.65
6.98
6.35
6.26
5.79
5.61
5.77
5.33
5.38
252y0581s 12/5/05
Predictor
Constant
X1
Coef
54.525
0.7490
S = 12.0764
SE Coef
2.384
0.1225
R-Sq = 32.4%
T
22.87
6.11
P
0.000
0.000
R-Sq(adj) = 31.5%
Analysis of Variance
Source
DF
SS
Regression
1
5451.3
Residual Error 78 11375.5
Total
79 16826.8
MS
5451.3
145.8
F
37.38
P
0.000
Durbin-Watson statistic = 0.0951522
MTB >
SUBC>
SUBC>
SUBC>
Regress c2 2 c3 c4;
VIF;
DW;
Brief 2.
Regression Analysis: Y versus X1, X2
The regression equation is
Y = 48.6 + 0.476 X1 + 2.51 X2
Predictor
Constant
X1
X2
Coef
48.610
0.4764
2.5067
S = 9.86336
SE Coef
2.161
0.1090
0.3967
R-Sq = 55.5%
T
22.50
4.37
6.32
P
0.000
0.000
0.000
VIF
1.2
1.2
R-Sq(adj) = 54.3%
Analysis of Variance
Source
Regression
Residual Error
Total
Source
X1
X2
DF
1
1
DF
2
77
79
SS
9335.8
7491.0
16826.8
MS
4667.9
97.3
F
47.98
P
0.000
Seq SS
5451.3
3884.5
Unusual Observations
Obs
X1
Y
Fit
50 -4.2 63.70 67.00
51 -8.2 61.93 66.44
SE Fit
3.38
3.91
Residual
-3.30
-4.52
St Resid
-0.36 X
-0.50 X
X denotes an observation whose X value gives it large influence.
Durbin-Watson statistic = 0.0952666
MTB > print c5-c10
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
Ysq
1925.31
1840.94
1906.64
1909.43
1996.68
2164.20
2247.47
2373.69
2590.11
2683.21
2741.80
3001.57
3262.17
X1sq
22.59
5.00
13.68
8.46
44.44
100.68
101.07
241.15
263.15
407.03
417.73
636.59
838.08
X2sq
5.4289
4.7089
11.9025
9.3025
5.2900
5.1076
5.8564
7.1824
5.8564
10.6929
10.3684
7.1289
8.9401
X1Y
208.57
95.90
161.53
127.10
297.88
466.78
476.60
756.58
825.58
1045.05
1070.20
1382.31
1653.47
X2Y
102.236
93.106
150.645
133.276
102.774
105.137
114.726
130.571
123.161
169.385
168.606
146.280
170.775
X1X2
11.075
4.850
12.762
8.871
15.333
22.676
24.329
41.618
39.257
65.972
65.812
67.366
86.559
252y0581s 12/5/05
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
74
75
76
77
78
79
80
3318.41
3298.91
3232.89
3082.33
2994.41
2890.04
2572.19
2266.30
2203.44
2315.32
2402.23
2606.37
2695.58
2751.83
3041.82
3265.81
3640.19
3736.24
3874.81
3938.20
4531.55
4794.30
4998.96
5078.09
4998.25
5180.79
5084.80
4941.91
4119.35
4200.35
4540.37
4606.69
4667.75
4668.66
4635.21
4355.41
4057.73
3834.78
3821.70
3992.12
4305.46
4834.85
5416.90
5761.80
6246.71
6517.90
6755.89
6858.13
7032.18
6919.16
7183.63
7204.72
7169.99
7088.90
7182.22
6902.40
7151.51
7459.17
7458.59
7437.44
7732.21
7791.66
7947.76
8107.22
8129.60
8415.77
8141.42
596.85
453.99
150.05
6.94
1.28
0.40
53.02
12.21
0.05
28.92
277.59
377.65
273.06
236.02
275.65
223.30
437.91
536.01
428.17
282.17
808.95
788.54
939.89
1013.08
163.74
244.19
135.13
119.93
0.69
0.01
5.22
11.80
214.92
72.27
0.59
8.29
17.86
67.06
6.69
92.81
302.86
951.90
922.62
813.40
979.20
702.75
770.55
1146.44
789.63
1060.22
710.53
534.20
538.27
492.63
546.46
256.86
403.49
372.73
351.92
857.41
812.28
569.51
855.69
557.46
471.63
706.90
367.47
4.4944
1.6641
0.5776
0.0576
0.0400
0.6084
1.7424
4.7524
1.3456
0.0121
1.4884
4.8841
6.1504
9.9225
8.0656
3.7249
2.5921
2.7889
1.9600
3.7249
2.7889
2.3409
2.5600
2.8224
1.2769
0.1849
2.1904
4.2849
10.8241
4.8400
6.8644
6.8121
16.3216
25.7049
50.2681
66.5856
66.2596
75.1689
48.4416
51.6961
55.0564
71.4025
79.0321
70.5600
78.4996
94.4784
81.7216
74.1321
82.0836
67.2400
67.8976
62.2521
44.6224
43.6921
43.2964
33.1776
38.6884
43.8244
58.5225
48.7204
40.3225
39.1876
33.5241
31.4721
33.2929
28.4089
28.9444
1407.33
1223.80
696.48
146.31
61.96
-34.10
-369.28
-166.34
11.00
258.78
816.60
992.11
857.94
805.91
915.68
853.97
1262.57
1415.15
1288.05
1054.15
1914.63
1944.35
2167.60
2268.15
904.66
1124.76
828.93
769.86
53.25
7.60
153.89
233.18
1001.60
580.88
52.50
-190.02
-269.21
-507.11
159.90
608.68
1141.91
2145.30
2235.57
2164.86
2473.21
2140.20
2281.61
2804.00
2356.45
2708.47
2259.25
1961.83
1964.54
1868.75
1981.10
1331.51
1698.69
1667.41
1620.14
2525.25
2506.14
2106.52
2607.84
2125.90
1958.11
2439.08
1729.66
122.124
74.093
43.212
13.324
-10.944
-41.932
-66.946
-103.780
-54.451
-5.293
59.795
112.826
128.759
165.242
156.634
110.294
97.138
102.078
87.147
121.117
112.419
105.939
113.125
119.718
79.889
30.950
105.536
145.518
211.159
142.582
176.542
177.147
276.016
346.421
482.704
538.523
518.520
536.895
430.267
454.287
486.871
587.555
654.300
637.615
700.260
784.730
743.036
713.027
759.754
682.088
698.392
669.708
565.634
556.533
557.642
478.545
526.004
571.746
660.678
601.959
558.375
552.573
516.180
505.125
520.248
488.961
485.436
51.793
27.486
9.310
0.632
-0.226
0.495
9.611
7.617
-0.272
-0.592
20.327
42.947
40.981
48.393
47.151
28.841
33.692
38.664
28.969
32.420
47.498
42.964
49.052
53.473
14.459
6.719
17.205
22.669
2.729
0.258
5.984
8.967
59.227
43.102
5.467
-23.495
-34.401
-70.999
18.002
69.266
129.130
260.707
270.031
239.569
277.248
257.671
250.940
291.527
254.590
267.000
219.644
182.360
154.981
146.711
153.817
92.314
124.941
127.807
143.511
204.385
180.979
149.391
169.370
132.455
125.308
141.712
103.132
252y0581s 12/5/05
MTB > sum c2
Sum of Y
Sum of Y = 5323.20
MTB > sum c3
Sum of X1
Sum of X1 = 1283.42
MTB > sum c4
Sum of X2
Sum of X2 = 328.33
MTB > sum c5
Sum of Ysq
Sum of Ysq = 371032
MTB > sum c6
Sum of X1sq
Sum of X1sq = 30307.6
MTB > sum c7
Sum of X2sq
Sum of X2sq = 2080.65
MTB > sum c8
Sum of X1Y
Sum of X1Y = 92676.9
MTB > sum c9
Sum of X2Y
Sum of X2Y = 24188.2
MTB > sum c10
Sum of X1X2
Sum of X1X2 = 6324.09
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x050812B.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x05081-2B.MTW'
Existing file replaced.
Spare Parts Computation – Y, X1, X2 in Columns 1-3.
MTB > exec '252OLS2'
Executing from file: 252OLS2.MTB
Regression Analysis: y versus x1
The regression equation is
y = 54.5 + 0.749 x1
Predictor
Constant
x1
S = 12.0764
Coef
54.525
0.7490
SE Coef
2.384
0.1225
R-Sq = 32.4%
T
22.87
6.11
P
0.000
0.000
R-Sq(adj) = 31.5%
252y0581s 12/5/05
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
78
79
SS
5451.3
11375.5
16826.8
MS
5451.3
145.8
F
37.38
P
0.000
Regression Analysis: y versus x1, x2
The regression equation is
y = 48.6 + 0.476 x1 + 2.51 x2
Predictor
Constant
x1
x2
Coef
48.610
0.4764
2.5067
S = 9.86336
SE Coef
2.161
0.1090
0.3967
R-Sq = 55.5%
T
22.50
4.37
6.32
P
0.000
0.000
0.000
R-Sq(adj) = 54.3%
Analysis of Variance
Source
Regression
Residual Error
Total
Source
x1
x2
DF
1
1
DF
2
77
79
SS
9335.8
7491.0
16826.8
MS
4667.9
97.3
F
47.98
P
0.000
Seq SS
5451.3
3884.5
Unusual Observations
Obs
50
51
x1
-4.2
-8.2
y
63.70
61.93
Fit
67.00
66.44
SE Fit
3.38
3.91
Residual
-3.30
-4.52
St Resid
-0.36 X
-0.50 X
X denotes an observation whose X value gives it large influence.
Executing from file: 252OLS2namer.MTB
Executing from file: 252OLS2sumer.MTB
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
y
43.8783
42.9062
43.6651
43.6970
44.6842
46.5210
47.4075
48.7205
50.8931
51.7997
52.3622
54.7866
57.1154
57.6056
57.4361
56.8585
x1
4.7533
2.2352
3.6992
2.9086
6.6664
10.0337
10.0533
15.5290
16.2219
20.1749
20.4385
25.2308
28.9496
24.4305
21.3071
12.2494
x2
2.33
2.17
3.45
3.05
2.30
2.26
2.42
2.68
2.42
3.27
3.22
2.67
2.99
2.12
1.29
0.76
252y0581s 12/5/05
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
74
75
76
77
78
79
80
55.5187
54.7212
53.7591
50.7168
47.6057
46.9408
48.1178
49.0126
51.0526
51.9190
52.4579
55.1527
57.1473
60.3340
61.1248
62.2480
62.7551
67.3168
69.2409
70.7033
71.2607
70.6983
71.9777
71.3078
70.2987
64.1822
64.8101
67.3823
67.8726
68.3209
68.3276
68.0824
65.9955
63.7003
61.9256
61.8199
63.1832
65.6160
69.5331
73.5996
75.9065
79.0361
80.7335
82.1942
82.8138
83.8581
83.1815
84.7563
84.8806
84.6758
84.1956
84.7480
83.0807
84.5666
86.3665
86.3631
86.2406
87.9330
88.2704
89.1502
90.0401
90.1643
91.7375
90.2298
Data Display
2.6353
1.1322
-0.6344
-7.2813
-3.4942
0.2343
5.3780
16.6611
19.4331
16.5245
15.3630
16.6026
14.9433
20.9264
23.1518
20.6922
16.7978
28.4421
28.0809
30.6577
31.8289
12.7960
15.6265
11.6247
10.9513
0.8296
0.1172
2.2839
3.4356
14.6602
8.5014
0.7711
-2.8793
-4.2262
-8.1891
2.5865
9.6336
17.4029
30.8529
30.3747
28.5201
31.2921
26.5094
27.7588
33.8591
28.1004
32.5610
26.6558
23.1128
23.2007
22.1953
23.3764
16.0267
20.0870
19.3062
18.7596
29.2815
28.5006
23.8644
29.2522
23.6106
21.7171
26.5876
19.1695
0.24
-0.20
-0.78
-1.32
-2.18
-1.16
-0.11
1.22
2.21
2.48
3.15
2.84
1.93
1.61
1.67
1.40
1.93
1.67
1.53
1.60
1.68
1.13
0.43
1.48
2.07
3.29
2.20
2.62
2.61
4.04
5.07
7.09
8.16
8.14
8.67
6.96
7.19
7.42
8.45
8.89
8.40
8.86
9.72
9.04
8.61
9.06
8.20
8.24
7.89
6.68
6.61
6.58
5.76
6.22
6.62
7.65
6.98
6.35
6.26
5.79
5.61
5.77
5.33
5.38
252y0581s 12/5/05
Row
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
x1sq
22.59
5.00
13.68
8.46
44.44
100.68
101.07
241.15
263.15
407.03
417.73
636.59
838.08
596.85
453.99
150.05
6.94
1.28
0.40
53.02
12.21
0.05
28.92
277.59
377.65
273.06
236.02
275.65
223.30
437.91
536.01
428.17
282.17
808.95
788.54
939.89
1013.08
163.74
244.19
135.13
119.93
0.69
0.01
5.22
11.80
214.92
72.27
0.59
8.29
17.86
67.06
6.69
92.81
302.86
951.90
922.62
813.40
979.20
702.75
770.55
1146.44
789.63
1060.22
710.53
534.20
538.27
x2sq
5.4289
4.7089
11.9025
9.3025
5.2900
5.1076
5.8564
7.1824
5.8564
10.6929
10.3684
7.1289
8.9401
4.4944
1.6641
0.5776
0.0576
0.0400
0.6084
1.7424
4.7524
1.3456
0.0121
1.4884
4.8841
6.1504
9.9225
8.0656
3.7249
2.5921
2.7889
1.9600
3.7249
2.7889
2.3409
2.5600
2.8224
1.2769
0.1849
2.1904
4.2849
10.8241
4.8400
6.8644
6.8121
16.3216
25.7049
50.2681
66.5856
66.2596
75.1689
48.4416
51.6961
55.0564
71.4025
79.0321
70.5600
78.4996
94.4784
81.7216
74.1321
82.0836
67.2400
67.8976
62.2521
44.6224
ysq
1925.31
1840.94
1906.64
1909.43
1996.68
2164.20
2247.47
2373.69
2590.11
2683.21
2741.80
3001.57
3262.17
3318.41
3298.91
3232.89
3082.33
2994.41
2890.04
2572.19
2266.30
2203.44
2315.32
2402.23
2606.37
2695.58
2751.83
3041.82
3265.81
3640.19
3736.24
3874.81
3938.20
4531.55
4794.30
4998.96
5078.09
4998.25
5180.79
5084.80
4941.91
4119.35
4200.35
4540.37
4606.69
4667.75
4668.66
4635.21
4355.41
4057.73
3834.78
3821.70
3992.12
4305.46
4834.85
5416.90
5761.80
6246.71
6517.90
6755.89
6858.13
7032.18
6919.16
7183.63
7204.72
7169.99
x1y
208.57
95.90
161.53
127.10
297.88
466.78
476.60
756.58
825.58
1045.05
1070.20
1382.31
1653.47
1407.33
1223.80
696.48
146.31
61.96
-34.10
-369.28
-166.34
11.00
258.78
816.60
992.11
857.94
805.91
915.68
853.97
1262.57
1415.15
1288.05
1054.15
1914.63
1944.35
2167.60
2268.15
904.66
1124.76
828.93
769.86
53.25
7.60
153.89
233.18
1001.60
580.88
52.50
-190.02
-269.21
-507.11
159.90
608.68
1141.91
2145.30
2235.57
2164.86
2473.21
2140.20
2281.61
2804.00
2356.45
2708.47
2259.25
1961.83
1964.54
x2y
102.236
93.106
150.645
133.276
102.774
105.137
114.726
130.571
123.161
169.385
168.606
146.280
170.775
122.124
74.093
43.212
13.324
-10.944
-41.932
-66.946
-103.780
-54.451
-5.293
59.795
112.826
128.759
165.242
156.634
110.294
97.138
102.078
87.147
121.117
112.419
105.939
113.125
119.718
79.889
30.950
105.536
145.518
211.159
142.582
176.542
177.147
276.016
346.421
482.704
538.523
518.520
536.895
430.267
454.287
486.871
587.555
654.300
637.615
700.260
784.730
743.036
713.027
759.754
682.088
698.392
669.708
565.634
x1x2
11.075
4.850
12.762
8.871
15.333
22.676
24.329
41.618
39.257
65.972
65.812
67.366
86.559
51.793
27.486
9.310
0.632
-0.226
0.495
9.611
7.617
-0.272
-0.592
20.327
42.947
40.981
48.393
47.151
28.841
33.692
38.664
28.969
32.420
47.498
42.964
49.052
53.473
14.459
6.719
17.205
22.669
2.729
0.258
5.984
8.967
59.227
43.102
5.467
-23.495
-34.401
-70.999
18.002
69.266
129.130
260.707
270.031
239.569
277.248
257.671
250.940
291.527
254.590
267.000
219.644
182.360
154.981
252y0581s 12/5/05
67
68
69
70
71
72
73
74
75
76
77
78
79
80
492.63
546.46
256.86
403.49
372.73
351.92
857.41
812.28
569.51
855.69
557.46
471.63
706.90
367.47
43.6921
43.2964
33.1776
38.6884
43.8244
58.5225
48.7204
40.3225
39.1876
33.5241
31.4721
33.2929
28.4089
28.9444
7088.90
7182.22
6902.40
7151.51
7459.17
7458.59
7437.44
7732.21
7791.66
7947.76
8107.22
8129.60
8415.77
8141.42
1868.75
1981.10
1331.51
1698.69
1667.41
1620.14
2525.25
2506.14
2106.52
2607.84
2125.90
1958.11
2439.08
1729.66
556.533
557.642
478.545
526.004
571.746
660.678
601.959
558.375
552.573
516.180
505.125
520.248
488.961
485.436
146.711
153.817
92.314
124.941
127.807
143.511
204.385
180.979
149.391
169.370
132.455
125.308
141.712
103.132
Data Display
sumy
sumx1
sumx2
n
smx1sq
smx2sq
smysq
smx1y
smx2y
smx1x2
5323.20
1283.42
328.330
80.0000
30307.6
2080.65
371032
92676.9
24188.2
6324.09
Executing from file: 252OLS2mean.MTB
Data Display
ybar
x1bar
x2bar
66.5400
16.0427
4.10413
Executing from file: 252OLS2ss.MTB
Data Display
SSx1
SSx2
SSy
Sx1y
Sx2y
Sx1x2
9718.15
733.144
16826.8
7278.52
2341.17
1056.80
If you need them, means and spare parts are below.
5323 .20
Y 
 66 .5400
X 22  nX 22  SSX 2  733 .16
80
1283 .42
Y 2  nY 2  SST  SSY  16826 .8
X1 
 16 .0428
80
X 1Y  nX 1Y  SX 1Y  7277 .87
328 .33
X2 
 4.1041
X 2 Y  nX 2 Y  SX 2Y  2341 .25
80
X
2
1
 nX 12  SSX1  9717 .86




X
1X 2
 nX 1 X 2  SX 1X 2  1056 .79
252y0582s
The 2nd and 3rd Normal equations are
7277 .87  9717 .86 b1
2341 .25  1056 .79 b1
1056 .79 b2
 733 .16 b2
7277 .87
1056 .79
 1.44142 , multiply Equation (3) by 1.44142.
3374 .72
733 .16
Now, subtract Equation 3' from Equation (1)
2
. Since
3
 9717 .86 b1
 1523 .28b1
3903 .15  8194 .58b1
1056 .79 b2
 1056 .79 b2
2
3'
0b2
3903 .15
 0.4763 . Now, substitute 0.4763 into either Equation (2) or Equation (3). We get
8194 .58
7277 .87  9717 .860.4763   1056 .79b2 2" or
So b1 
2341 .25  1056 .790.4763   733 .16b2
3"
Using 2" , we get 1056 .79b2  7277 .87  4628 .62 . So b2 
2649 .65
 2.5069 or, using 3" , we get
1056 .79
1837 .90
 2.5068 The difference is due to rounding.
733 .16
Finally, since Y  b0  b1 X 1  b2 X 2 , we can write b0  Y  b1 X 1  b2 X 2
733 .16b2  2341 .25  503 .35 . So b2 
 66.5400  0.4763 16.0428  2.5068 4.1041  66.5400  7.6412  10.2882  48.6106 . Our equation is
thus Yˆ  48.611 0.476X  2.507X
1
2
17
252y0582s
Caniglia’s Original Data
Data Display
Row
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
STATE
ME
NH
VT
MA
RI
CT
NY
NJ
PA
OH
IN
IL
MI
WI
MN
IA
MO
ND
SD
NE
KS
DE
MD
DC
VA
WV
NC
SC
GA
FL
KY
TN
AL
MS
AR
LA
OK
TX
MT
ID
WY
CO
NM
AZ
UT
NV
WA
OR
CA
AK
HI
MIM
12112
14505
12711
15362
13911
17938
15879
17639
15225
16164
15793
17551
17137
15417
15878
15249
14743
13835
12406
14873
15504
16081
17321
15861
15506
13998
12529
12660
13966
14651
13328
13349
13301
11968
12274
15365
14818
16135
14256
14297
17615
16672
14057
15269
15788
16820
17042
15833
17128
21552
15268
PMHS
69.1
73.0
71.6
74.0
65.1
71.8
68.9
70.0
68.0
69.0
68.8
68.9
69.3
70.9
73.5
71.9
66.2
68.0
68.3
74.2
74.5
70.4
69.2
67.9
64.3
58.6
58.2
58.2
60.4
68.0
55.8
59.0
59.9
57.2
58.3
61.3
68.7
65.3
73.8
73.5
77.9
79.1
70.6
73.4
80.4
76.0
77.5
75.1
74.3
81.9
76.9
PURBAN
47.5
52.2
33.8
83.8
87.0
78.8
84.6
89.0
69.3
73.3
64.2
83.3
70.7
64.2
66.9
58.6
68.1
48.8
46.4
62.9
66.7
70.6
80.3
100.0
66.0
36.2
48.0
54.1
62.4
84.3
50.9
60.4
60.0
47.3
51.6
68.6
67.3
79.6
52.9
54.0
62.7
80.6
72.1
83.8
84.4
85.3
73.5
67.9
91.3
64.3
86.5
MAGE
29.2
29.2
28.4
29.6
30.1
30.6
30.3
30.7
30.4
28.6
28.0
28.6
27.8
28.3
28.3
28.7
29.3
27.5
27.9
28.6
28.7
28.7
29.2
29.9
28.6
29.1
28.1
26.7
27.3
32.9
27.8
28.7
27.8
26.1
29.2
26.2
28.6
27.1
28.4
27.0
26.7
27.9
26.6
28.2
23.8
30.0
29.0
29.5
28.9
26.3
27.6
NE
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
MW
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
SO
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
18