252y0541s 5/7/05
ECO252 QBA2, Final EXAM, May 4, 2005
Preparatory Computations
Part I Regression problem.
————— 4/28/2005 6:18:32 PM ————————————————————
Welcome to Minitab, press F1 for help.
Results for: 252x0504-4.MTW
MTB > Stepwise 'MPG' 'Horsepower' 'Length' 'Width' 'Weight' 'Cargo Volume' &
CONT>
'Turning Circle' 'SUV_D' 'Fuel_D' 'SUVwt' 'HPsq' 'AWD_D' &
CONT>
'FWD_D' 'RWD_D' 'SUV_L';
SUBC>
AEnter 0.15;
SUBC>
ARemove 0.15;
SUBC>
Best 0;
SUBC>
Constant.
Stepwise Regression: MPG versus Horsepower, Length, ...
Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15
Response is MPG on 14 predictors, with N = 119
N(cases with missing observations) = 2 N(all cases) = 121
Step
Constant
Weight
T-Value
P-Value
1
38.31
2
36.75
3
41.59
4
50.06
5
50.15
6
59.00
-0.00491
-15.34
0.000
-0.00436
-11.87
0.000
-0.00578
-12.82
0.000
-0.00495
-9.31
0.000
-0.00424
-6.74
0.000
-0.00339
-5.61
0.000
-1.72
-2.84
0.005
-33.71
-4.99
0.000
-35.29
-5.36
0.000
-35.12
-5.40
0.000
-18.68
-2.71
0.008
0.180
4.75
0.000
0.185
5.04
0.000
0.182
5.01
0.000
0.088
2.26
0.026
-0.285
-2.79
0.006
-0.292
-2.90
0.004
-0.255
-2.75
0.007
-0.0124
-2.01
0.046
-0.1619
-5.04
0.000
SUV_D
T-Value
P-Value
SUV_L
T-Value
P-Value
Turning Circle
T-Value
P-Value
Horsepower
T-Value
P-Value
HPsq
T-Value
P-Value
S
R-Sq
R-Sq(adj)
Mallows C-p
0.00040
4.73
0.000
2.50
66.78
66.50
71.5
2.43
68.94
68.40
61.4
2.23
74.04
73.36
34.8
2.17
75.70
74.85
27.4
2.14
76.55
75.51
24.7
1.96
80.45
79.41
4.8
More? (Yes, No, Subcommand, or Help)
SUBC> y
1
252y0541s 5/7/05
Step
Constant
7
58.50
Weight
T-Value
P-Value
-0.00342
-5.74
0.000
SUV_D
T-Value
P-Value
-19.0
-2.79
0.006
SUV_L
T-Value
P-Value
0.090
2.36
0.020
Turning Circle
T-Value
P-Value
-0.210
-2.24
0.027
Horsepower
T-Value
P-Value
-0.175
-5.43
0.000
HPsq
T-Value
P-Value
0.00042
5.03
0.000
Fuel_D
T-Value
P-Value
0.92
2.11
0.037
S
R-Sq
R-Sq(adj)
Mallows C-p
1.93
81.21
80.02
2.5
More? (Yes, No, Subcommand, or Help)
SUBC> y
No variables entered or removed
More? (Yes, No, Subcommand, or Help)
SUBC> n
2
252y0541s 5/7/05
MTB > Correlation 'Horsepower' 'Length' 'Width' 'Weight' 'Cargo Volume' &
CONT>
'Turning Circle' 'SUV_D' 'Fuel_D' 'SUVwt' 'SUVtc' 'HPsq' 'AWD_D' &
CONT>
'FWD_D' 'RWD_D' 'SUV_L'.
Correlations: Horsepower, Length, Width, Weight, Cargo Volume, ...
Horsepower
0.648
0.000
Length
Width
0.660
0.000
0.825
0.000
Weight
0.673
0.000
0.634
0.000
0.780
0.000
Cargo Volume
0.296
0.001
0.395
0.000
0.546
0.000
0.716
0.000
Turning Circ
0.497
0.000
0.750
0.000
0.658
0.000
0.650
0.000
SUV_D
0.160
0.080
-0.102
0.265
0.180
0.049
0.535
0.000
Fuel_D
0.321
0.000
-0.013
0.886
-0.042
0.645
0.057
0.540
SUVwt
0.182
0.045
-0.077
0.403
0.206
0.023
0.562
0.000
SUVtc
0.185
0.042
-0.062
0.502
0.211
0.020
0.577
0.000
HPsq
0.989
0.000
0.632
0.000
0.645
0.000
0.668
0.000
AWD_D
0.059
0.523
-0.118
0.199
-0.037
0.691
0.065
0.483
FWD_D
-0.370
0.000
-0.001
0.994
-0.163
0.076
-0.453
0.000
RWD_D
0.334
0.000
0.070
0.445
0.151
0.101
0.351
0.000
SUV_L
0.197
0.030
-0.053
0.564
0.219
0.016
0.582
0.000
Cargo Volume
0.486
0.000
Turning Circ
SUV_D
Fuel_D
0.459
0.000
0.139
0.127
-0.245
0.007
-0.069
0.456
-0.147
0.110
SUVwt
0.473
0.000
0.161
0.078
0.999
0.000
-0.141
0.125
SUVtc
0.484
0.000
0.196
0.031
0.996
0.000
-0.142
0.121
Length
Turning Circ
SUV_D
Fuel_D
Width
Weight
3
252y0541s 5/7/05
HPsq
0.289
0.001
0.480
0.000
0.173
0.058
0.296
0.001
AWD_D
0.021
0.823
-0.068
0.461
0.185
0.043
0.218
0.017
FWD_D
-0.165
0.071
-0.027
0.771
-0.517
0.000
-0.280
0.002
RWD_D
0.108
0.239
0.015
0.874
0.364
0.000
0.098
0.288
SUV_L
0.487
0.000
0.181
0.047
0.996
0.000
-0.145
0.114
SUVwt
0.998
0.000
SUVtc
HPsq
AWD_D
HPsq
0.198
0.030
0.200
0.028
AWD_D
0.184
0.044
0.174
0.057
0.040
0.667
FWD_D
-0.522
0.000
-0.526
0.000
-0.369
0.000
-0.366
0.000
RWD_D
0.367
0.000
0.374
0.000
0.347
0.000
-0.137
0.135
SUV_L
0.999
0.000
0.998
0.000
0.215
0.018
0.176
0.054
FWD_D
-0.810
0.000
RWD_D
-0.529
0.000
0.381
0.000
SUVtc
RWD_D
SUV_L
Cell Contents: Pearson correlation
P-Value
PRESS
Assesses your model's predictive ability. In general, the smaller the prediction sum of squares (PRESS) value, the
better the model's predictive ability. PRESS is used to calculate the predicted R 2. PRESS, similar to the error sum of
squares (SSE), is the sum of squares of the prediction error. PRESS differs from SSE in that each fitted value, i, for
PRESS is obtained by deleting the ith observation from the data set, estimating the regression equation from the
remaining n - 1 observations, then using the fitted regression function to obtain the predicted value for the i th
observation.
Predicted R2
Similar to R2. Predicted R2 indicates how well the model predicts responses for new observations, whereas R 2 indicates
how well the model fits your data. Predicted R2 can prevent overfitting the model and is more useful than adjusted R2
for comparing models because it is calculated with observations not included in model calculation.
Predicted R2 is between 0 and 1 and is calculated from the PRESS statistic. Larger values of predicted R 2 suggest
models of greater predictive ability.
4
252y0541s 5/7/05
MTB > Regress 'MPG' 6 'Weight' 'SUV_D' 'SUV_L' 'Turning Circle'
CONT>
'Horsepower' 'HPsq';
SUBC>
Constant;
SUBC>
Brief 2.
&
MTB > Regress 'MPG' 6 'Weight' 'SUV_D' 'SUV_L' 'Turning Circle'
CONT>
'Horsepower' 'HPsq';
SUBC>
GNormalplot;
SUBC>
NoDGraphs;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
Press;
SUBC>
Brief 2.
&
Regression Analysis: MPG versus Weight, SUV_D, ...
The regression equation is
MPG = 63.1 - 0.00303 Weight - 14.8 SUV_D + 0.0653 SUV_L - 0.264 Turning Circle
- 0.213 Horsepower + 0.000522 HPsq
Predictor
Constant
Weight
SUV_D
SUV_L
Turning Circle
Horsepower
HPsq
Coef
63.105
-0.0030345
-14.812
0.06527
-0.2639
-0.21251
0.00052249
SE Coef
3.978
0.0006859
7.957
0.04478
0.1050
0.03575
0.00009459
T
15.86
-4.42
-1.86
1.46
-2.51
-5.94
5.52
P
0.000
0.000
0.065
0.148
0.013
0.000
0.000
VIF
5.6
282.1
307.9
2.0
63.5
61.3
S = 2.27485
R-Sq = 77.5%
R-Sq(adj) = 76.4%
PRESS = 752.906
R-Sq(pred) = 71.34%
Analysis of Variance
Source
DF
SS
Regression
6 2037.34
Residual Error 114
589.95
Total
120 2627.29
Source
Weight
SUV_D
SUV_L
Turning Circle
Horsepower
HPsq
DF
1
1
1
1
1
1
MS
339.56
5.17
F
65.62
P
0.000
Unusual Observations
Obs Weight
MPG
16
5590 13.000
34
7270 10.000
40
5590 13.000
62
4065 19.000
108
2150 38.000
111
2750 41.000
114
2935 41.000
115
2940 24.000
Seq SS
1605.19
47.29
132.83
52.31
41.83
157.89
Fit
15.361
6.856
15.361
14.633
30.489
33.473
29.806
29.791
SE Fit
1.137
1.461
1.137
0.654
0.632
1.133
0.777
0.778
Residual
-2.361
3.144
-2.361
4.367
7.511
7.527
11.194
-5.791
St Resid
-1.20 X
1.80 X
-1.20 X
2.00R
3.44R
3.82RX
5.24R
-2.71R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > Regress 'MPG' 5 'Weight' 'SUV_D'
CONT>
'HPsq';
SUBC>
GNormalplot;
SUBC>
NoDGraphs;
SUBC>
RType 1;
'Turning Circle' 'Horsepower'
&
5
252y0541s 5/7/05
SUBC>
SUBC>
SUBC>
SUBC>
Constant;
VIF;
Press;
Brief 2.
Regression Analysis: MPG versus Weight, SUV_D, ...
The regression equation is
MPG = 63.1 - 0.00250 Weight - 3.25 SUV_D - 0.250 Turning Circle
- 0.239 Horsepower + 0.000593 HPsq
Predictor
Constant
Weight
SUV_D
Turning Circle
Horsepower
HPsq
Coef
63.137
-0.0025020
-3.2492
-0.2501
-0.23928
0.00059313
SE Coef
3.998
0.0005834
0.6272
0.1051
0.03082
0.00008163
T
15.79
-4.29
-5.18
-2.38
-7.76
7.27
P
0.000
0.000
0.000
0.019
0.000
0.000
VIF
4.0
1.7
1.9
46.7
45.2
S = 2.28595
R-Sq = 77.1%
R-Sq(adj) = 76.1%
PRESS = 744.047
R-Sq(pred) = 71.68%
Analysis of Variance
Source
DF
SS
Regression
5 2026.35
Residual Error 115
600.94
Total
120 2627.29
Source
Weight
SUV_D
Turning Circle
Horsepower
HPsq
DF
1
1
1
1
1
MS
405.27
5.23
F
77.56
P
0.000
Seq SS
1605.19
47.29
46.32
51.65
275.90
Unusual Observations
Obs
16
34
40
108
111
114
115
Weight
5590
7270
5590
2150
2750
2935
2940
MPG
13.000
10.000
13.000
38.000
41.000
41.000
24.000
Fit
14.381
5.945
14.381
30.081
33.910
30.060
30.047
SE Fit
0.921
1.328
0.921
0.570
1.098
0.761
0.762
Residual
-1.381
4.055
-1.381
7.919
7.090
10.940
-6.047
St Resid
-0.66 X
2.18RX
-0.66 X
3.58R
3.54RX
5.08R
-2.81R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > Stepwise 'MPG' 'Horsepower' 'Length' 'Width' 'Weight' 'Cargo Volume' &
CONT>
'Turning Circle' 'SUV_D' 'Fuel_D' 'SUVwt' 'HPsq' 'AWD_D' &
CONT>
'FWD_D' 'RWD_D' 'SUV_L';
SUBC>
AEnter 0.15;
SUBC>
ARemove 0.15;
SUBC>
Best 0;
SUBC>
Constant.
6
252y0541s 5/7/05
Stepwise Regression: MPG versus Horsepower, Length, ...
Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15
Response is MPG on 14 predictors, with N = 119
N(cases with missing observations) = 2 N(all cases) = 121
Step
Constant
Weight
T-Value
P-Value
1
38.31
2
36.75
3
41.59
4
50.06
5
50.15
6
59.00
-0.00491
-15.34
0.000
-0.00436
-11.87
0.000
-0.00578
-12.82
0.000
-0.00495
-9.31
0.000
-0.00424
-6.74
0.000
-0.00339
-5.61
0.000
-1.72
-2.84
0.005
-33.71
-4.99
0.000
-35.29
-5.36
0.000
-35.12
-5.40
0.000
-18.68
-2.71
0.008
0.180
4.75
0.000
0.185
5.04
0.000
0.182
5.01
0.000
0.088
2.26
0.026
-0.285
-2.79
0.006
-0.292
-2.90
0.004
-0.255
-2.75
0.007
-0.0124
-2.01
0.046
-0.1619
-5.04
0.000
SUV_D
T-Value
P-Value
SUV_L
T-Value
P-Value
Turning Circle
T-Value
P-Value
Horsepower
T-Value
P-Value
HPsq
T-Value
P-Value
0.00040
4.73
0.000
S
R-Sq
R-Sq(adj)
Mallows C-p
2.50
66.78
66.50
71.5
2.43
68.94
68.40
61.4
2.23
74.04
73.36
34.8
2.17
75.70
74.85
27.4
2.14
76.55
75.51
24.7
1.96
80.45
79.41
4.8
More? (Yes, No, Subcommand, or Help)
SUBC> remove c20.
Step
Constant
7
59.15
8
59.00
9
58.50
Weight
T-Value
P-Value
-0.00267
-5.10
0.000
-0.00339
-5.61
0.000
-0.00342
-5.74
0.000
SUV_D
T-Value
P-Value
-3.13
-5.51
0.000
-18.68
-2.71
0.008
-18.95
-2.79
0.006
0.088
2.26
0.026
0.090
2.36
0.020
SUV_L
T-Value
P-Value
Turning Circle
T-Value
P-Value
-0.236
-2.51
0.013
-0.255
-2.75
0.007
-0.210
-2.24
0.027
Horsepower
T-Value
P-Value
-0.199
-7.09
0.000
-0.162
-5.04
0.000
-0.175
-5.43
0.000
0.00050
0.00040
0.00042
HPsq
7
252y0541s 5/7/05
T-Value
P-Value
6.75
0.000
4.73
0.000
Fuel_D
T-Value
P-Value
S
R-Sq
R-Sq(adj)
Mallows C-p
5.03
0.000
0.92
2.11
0.037
2.00
79.56
78.66
7.8
1.96
80.45
79.41
4.8
1.93
81.21
80.02
2.5
More? (Yes, No, Subcommand, or Help)
SUBC> enter c17 c18 c19.
Step
Constant
10
60.14
11
59.11
12
58.50
13
58.50
Weight
T-Value
P-Value
-0.00355
-5.75
0.000
-0.00346
-5.72
0.000
-0.00344
-5.72
0.000
-0.00342
-5.74
0.000
SUV_D
T-Value
P-Value
-19.5
-2.82
0.006
-19.1
-2.77
0.007
-18.8
-2.74
0.007
-19.0
-2.79
0.006
SUV_L
T-Value
P-Value
Turning Circle
T-Value
P-Value
0.092
2.37
0.020
-0.207
-2.10
0.038
0.090
2.32
0.022
-0.205
-2.09
0.039
0.089
2.30
0.023
-0.202
-2.07
0.041
0.090
2.36
0.020
-0.210
-2.24
0.027
Horsepower
T-Value
P-Value
-0.175
-5.33
0.000
-0.177
-5.42
0.000
-0.176
-5.41
0.000
-0.175
-5.43
0.000
HPsq
T-Value
P-Value
0.00042
4.98
0.000
0.00043
5.04
0.000
0.00042
5.02
0.000
0.00042
5.03
0.000
Fuel_D
T-Value
P-Value
0.73
1.49
0.139
0.80
1.66
0.099
0.87
1.92
0.057
0.92
2.11
0.037
AWD_D
T-Value
P-Value
-1.1
-0.76
0.451
FWD_D
T-Value
P-Value
-1.36
-0.98
0.331
-0.51
-0.62
0.535
-0.17
-0.32
0.752
RWD_D
T-Value
P-Value
-1.23
-0.93
0.353
-0.42
-0.55
0.586
S
R-Sq
R-Sq(adj)
Mallows C-p
1.95
81.37
79.65
7.6
1.95
81.27
79.73
6.1
1.94
81.22
79.86
4.4
1.93
81.21
80.02
2.5
More? (Yes, No, Subcommand, or Help)
SUBC> no
8
252y0541s 5/7/05
Results for: 252x0504-41.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x050441.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-41.MTW'
MTB > erase c21
MTB > Regress 'MPG' 6 'Weight' 'SUV_D' 'SUV_L' 'Turning Circle' &
CONT>
'Horsepower' 'HPsq' ;
SUBC>
GNormalplot;
SUBC>
NoDGraphs;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
Press;
SUBC>
Brief 2.
Regression Analysis: MPG versus Weight, SUV_D, ...
The regression equation is
MPG = 64.4 - 0.00284 Weight - 15.8 SUV_D + 0.0694 SUV_L - 0.305 Turning Circle
- 0.214 Horsepower + 0.000524 HPsq
Predictor
Constant
Weight
SUV_D
SUV_L
Turning Circle
Horsepower
HPsq
Coef
64.364
-0.0028431
-15.843
0.06943
-0.3045
-0.21444
0.00052386
SE Coef
3.973
0.0006832
7.867
0.04423
0.1055
0.03528
0.00009332
T
16.20
-4.16
-2.01
1.57
-2.89
-6.08
5.61
P
0.000
0.000
0.046
0.119
0.005
0.000
0.000
VIF
5.7
276.4
301.7
2.0
63.1
61.0
S = 2.24427
R-Sq = 78.3%
R-Sq(adj) = 77.2%
PRESS = 725.963
R-Sq(pred) = 72.34%
Analysis of Variance
Source
DF
SS
Regression
6 2055.21
Residual Error 113
569.15
Total
119 2624.37
Source
Weight
SUV_D
SUV_L
Turning Circle
Horsepower
HPsq
DF
1
1
1
1
1
1
MS
342.54
5.04
F
68.01
P
0.000
Unusual Observations
Obs Weight
MPG
16
5590 13.000
34
7270 10.000
36
2715 24.000
40
5590 13.000
107
2150 38.000
110
2750 41.000
113
2935 41.000
114
2940 24.000
Seq SS
1602.61
49.58
135.39
61.04
47.88
158.71
Fit
15.259
6.907
28.432
15.259
30.543
33.747
30.000
29.985
SE Fit
1.123
1.442
0.493
1.123
0.624
1.126
0.772
0.774
Residual
-2.259
3.093
-4.432
-2.259
7.457
7.253
11.000
-5.985
St Resid
-1.16 X
1.80 X
-2.02R
-1.16 X
3.46R
3.74RX
5.22R
-2.84R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > Regress 'MPG' 5 'Weight' 'SUV_D'
CONT>
'HPsq' ;
SUBC>
GNormalplot;
SUBC>
NoDGraphs;
'Turning Circle' 'Horsepower'
&
9
252y0541s 5/7/05
SUBC>
SUBC>
SUBC>
SUBC>
SUBC>
RType 1;
Constant;
VIF;
Press;
Brief 2.
Regression Analysis: MPG versus Weight, SUV_D, ...
The regression equation is
MPG = 64.4 - 0.00228 Weight - 3.53 SUV_D - 0.288 Turning Circle
- 0.243 Horsepower + 0.000599 HPsq
Predictor
Constant
Weight
SUV_D
Turning Circle
Horsepower
HPsq
Coef
64.352
-0.0022848
-3.5330
-0.2884
-0.24278
0.00059879
SE Coef
3.999
0.0005871
0.6366
0.1057
0.03051
0.00008071
T
16.09
-3.89
-5.55
-2.73
-7.96
7.42
P
0.000
0.000
0.000
0.007
0.000
0.000
VIF
4.2
1.8
2.0
46.6
45.0
S = 2.25865
R-Sq = 77.8%
R-Sq(adj) = 76.9%
PRESS = 720.507
R-Sq(pred) = 72.55%
Analysis of Variance
Source
DF
SS
Regression
5 2042.80
Residual Error 114
581.57
Total
119 2624.37
Source
Weight
SUV_D
Turning Circle
Horsepower
HPsq
DF
1
1
1
1
1
MS
408.56
5.10
F
80.09
P
0.000
Unusual Observations
Obs Weight
MPG
16
5590 13.000
34
7270 10.000
40
5590 13.000
107
2150 38.000
110
2750 41.000
113
2935 41.000
114
2940 24.000
Seq SS
1602.61
49.58
52.45
57.33
280.82
Fit
14.223
5.938
14.223
30.108
34.201
30.262
30.251
SE Fit
0.914
1.312
0.914
0.563
1.095
0.759
0.760
Residual
-1.223
4.062
-1.223
7.892
6.799
10.738
-6.251
St Resid
-0.59 X
2.21RX
-0.59 X
3.61R
3.44RX
5.05R
-2.94R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > Regress 'MPG' 8 'Weight' 'SUV_D' 'Turning Circle' 'Horsepower'
CONT>
'HPsq' 'AWD_D' 'FWD_D' 'RWD_D';
SUBC>
GNormalplot;
SUBC>
NoDGraphs;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
Press;
SUBC>
Brief 2.
&
Regression Analysis: MPG versus Weight, SUV_D, ...
The regression equation is
MPG = 66.4 - 0.00248 Weight - 3.83 SUV_D - 0.254 Turning Circle
- 0.251 Horsepower + 0.000618 HPsq - 1.21 AWD_D - 2.10 FWD_D - 1.70 RWD_D
Predictor
Coef
SE Coef
T
P
VIF
10
252y0541s 5/7/05
Constant
Weight
SUV_D
Turning Circle
Horsepower
HPsq
AWD_D
FWD_D
RWD_D
66.435
-0.0024795
-3.8302
-0.2541
-0.25082
0.00061833
-1.213
-2.103
-1.697
4.400
0.0006077
0.6814
0.1116
0.03122
0.00008244
1.620
1.490
1.434
15.10
-4.08
-5.62
-2.28
-8.03
7.50
-0.75
-1.41
-1.18
0.000
0.000
0.000
0.025
0.000
0.000
0.455
0.161
0.239
4.4
2.0
2.2
48.6
46.7
3.4
11.2
8.6
S = 2.26416
R-Sq = 78.3%
R-Sq(adj) = 76.8%
PRESS = 727.840
R-Sq(pred) = 72.27%
Analysis of Variance
Source
DF
SS
Regression
8 2055.33
Residual Error 111
569.03
Total
119 2624.37
Source
Weight
SUV_D
Turning Circle
Horsepower
HPsq
AWD_D
FWD_D
RWD_D
DF
1
1
1
1
1
1
1
1
MS
256.92
5.13
F
50.12
P
0.000
Seq SS
1602.61
49.58
52.45
57.33
280.82
2.00
3.36
7.17
Unusual Observations
Obs
34
57
72
107
109
110
113
114
Weight
7270
4735
4720
2150
5435
2750
2935
2940
MPG
10.000
14.000
15.000
38.000
14.000
41.000
41.000
24.000
Fit
5.609
13.622
15.901
30.231
13.477
34.346
30.341
30.329
SE Fit
1.377
1.447
1.374
0.574
1.338
1.106
0.765
0.766
Residual
4.391
0.378
-0.901
7.769
0.523
6.654
10.659
-6.329
St Resid
2.44RX
0.22 X
-0.50 X
3.55R
0.29 X
3.37RX
5.00R
-2.97R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
11
252y0541s 5/7/05
Part II
1. Time series problem.
————— 4/28/2005 6:18:32 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05045.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-5.MTW'
Worksheet was saved on Fri Apr 29 2005
Results for: 252x0504-5.MTW
MTB > let c3=c2*c2
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x05045.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-5.MTW'
Existing file replaced.
MTB > Execute "C:\Documents and Settings\rbove\My Documents\Minitab\252OLS2.mtb"
1.
Executing from file: C:\Documents and Settings\rbove\My
Documents\Minitab\252OLS2.mtb
Regression Analysis: Y versus T
The regression equation is
Y = 56.7 + 1.54 T
Predictor
Constant
T
Coef
56.659
1.5377
S = 2.36169
SE Coef
1.283
0.1411
T
44.15
10.89
R-Sq = 90.1%
P
0.000
0.000
R-Sq(adj) = 89.4%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
13
14
SS
662.05
72.51
734.56
Unusual Observations
Obs
T
Y
Fit
1 1.0 53.430 58.196
MS
662.05
5.58
SE Fit
1.161
F
118.70
Residual
-4.766
P
0.000
St Resid
-2.32R
R denotes an observation with a large standardized residual.
Regression Analysis: Y versus T, TSQ
The regression equation is
Y = 52.4 + 3.04 T - 0.0939 TSQ
Predictor
Constant
T
TSQ
Coef
52.401
3.0405
-0.09392
S = 1.73483
SE Coef
1.545
0.4444
0.02701
R-Sq = 95.1%
T
33.91
6.84
-3.48
P
0.000
0.000
0.005
R-Sq(adj) = 94.3%
12
252y0541s 5/7/05
Analysis of Variance
Source
Regression
Residual Error
Total
Source
T
TSQ
DF
1
1
DF
2
12
14
SS
698.44
36.12
734.56
MS
349.22
3.01
F
116.03
P
0.000
Seq SS
662.05
36.39
Unusual Observations
Obs
5
T
5.0
Y
68.650
Fit
65.255
SE Fit
0.605
Residual
3.395
St Resid
2.09R
R denotes an observation with a large standardized residual.
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
Y
53.43
59.09
59.58
64.75
68.65
65.53
68.44
70.93
72.85
73.60
72.93
75.14
73.88
76.55
79.05
T
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TSQ
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
C4
x1sq
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
* NOTE * One or more variables are undefined.
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
x2sq
1
16
81
256
625
1296
2401
4096
6561
10000
14641
20736
28561
38416
50625
ysq
2854.76
3491.63
3549.78
4192.56
4712.82
4294.18
4684.03
5031.06
5307.12
5416.96
5318.78
5646.02
5458.25
5859.90
6248.90
x1y
53.43
118.18
178.74
259.00
343.25
393.18
479.08
567.44
655.65
736.00
802.23
901.68
960.44
1071.70
1185.75
x2y
53.4
236.4
536.2
1036.0
1716.3
2359.1
3353.6
4539.5
5900.9
7360.0
8824.5
10820.2
12485.7
15003.8
17786.3
x1x2
1
8
27
64
125
216
343
512
729
1000
1331
1728
2197
2744
3375
13
252y0541s 5/7/05
Data Display
sumy
sumx1
sumx2
n
smx1sq
smx2sq
smysq
smx1y
smx2y
smx1x2
1034.40
120.000
1240.00
15.0000
1240.00
178312
72066.8
8705.75
92011.7
14400.0
Executing from file: 252OLS2mean.MTB
Data Display
ybar
x1bar
x2bar
68.9600
8.00000
82.6667
Executing from file: 252OLS2ss.MTB
Data Display
SSx1
SSx2
SSy
Sx1y
Sx2y
Sx1x2
280.000
75805.3
734.556
430.550
6501.33
4480.00
MTB > print c1-c3
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Y
53.43
59.09
59.58
64.75
68.65
65.53
68.44
70.93
72.85
73.60
72.93
75.14
73.88
76.55
79.05
T
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TSQ
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
MTB >
14
252y0541s 5/7/05
Problem 4 - ANOVA etc
————— 4/28/2005 6:18:32 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB >
SUBC>
SUBC>
MTB >
MTB >
SUBC>
SUBC>
SUBC>
MTB >
Stack 'x1' 'x2' 'x3' 'x4' c10;
Subscripts c11;
UseNames.
Rank c10 c12.
Unstack (c12);
Subscripts c11;
After;
VarNames.
print c1-c5
Data Display
Row
1
2
3
4
5
Student
Loopy
Percival
Poopsy
Dizzy
Booger
x1
8.75
9.50
9.25
9.50
9.25
x2
9.5
4.0
5.5
8.5
4.5
x3
8.5
8.5
7.5
7.5
8.0
x4
11.5
11.0
7.5
7.5
8.0
MTB > print c1 c2 c6 c3 c7 c4 c8 c5 c9
Data Display
Row
1
2
3
4
5
Student
Loopy
Percival
Poopsy
Dizzy
Booger
x1
8.75
9.50
9.25
9.50
9.25
r1
13.0
17.0
14.5
17.0
14.5
x2
9.5
4.0
5.5
8.5
4.5
r2
17
1
3
11
2
x3
8.5
8.5
7.5
7.5
8.0
r3
11.0
11.0
5.5
5.5
8.5
x4
11.5
11.0
7.5
7.5
8.0
r4
20.0
19.0
5.5
5.5
8.5
MTB > let c13 = c2+c3+c4+c5
MTB > let c14 = (c2*c2) + (c3*c3) + (c4*c4) + (c5*c5)
MTB > sum c2
Sum of x1
Sum of x1 = 46.25
MTB > ssq c2
Sum of Squares of x1
Sum of squares (uncorrected) of x1 = 428.188
MTB > sum c3
Sum of x2
Sum of x2 = 32
MTB > ssq c3
Sum of Squares of x2
Sum of squares (uncorrected) of x2 = 229
MTB > sum c4
Sum of x3
Sum of x3 = 40
MTB > ssq c4
Sum of Squares of x3
Sum of squares (uncorrected) of x3 = 321
MTB > sum c5
Sum of x4
Sum of x4 = 45.5
15
252y0541s 5/7/05
MTB > ssq c5
Sum of Squares of x4
Sum of squares (uncorrected) of x4 = 429.75
MTB > print c13 c14
Data Display
Row
1
2
3
4
5
C13
38.25
33.00
29.75
33.00
29.75
C14
371.313
299.500
228.313
275.000
233.813
Results for: 252x0504-6.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05046.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-6.MTW'
MTB >
————— 5/5/2005 6:38:07 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05046a.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-6a.MTW'
Worksheet was saved on Thu May 05 2005
Results for: 252x0504-6a.MTW
MTB > print c1-c4
Data Display
Row
1
2
3
4
5
C1
8.75
9.50
9.25
9.50
9.25
C2
9.5
4.0
5.5
8.5
4.5
C3
8.5
8.5
7.5
7.5
8.0
C4
11.5
11.0
7.5
7.5
8.0
MTB > exec '2522way4'
Executing from file: 2522way4.MTB
Executing from file: 2522onw4.MTB
One-way ANOVA: C1, C2, C3, C4
Source
Factor
Error
Total
DF
3
16
19
S = 1.606
Level
C1
C2
C3
C4
N
5
5
5
5
SS
25.96
41.28
67.23
MS
8.65
2.58
F
3.35
R-Sq = 38.61%
Mean
9.250
6.400
8.000
9.100
StDev
0.306
2.460
0.500
1.981
P
0.045
R-Sq(adj) = 27.10%
Individual 95% CIs For Mean Based on
Pooled StDev
-------+---------+---------+---------+-(---------*---------)
(---------*---------)
(---------*---------)
(---------*---------)
16
252y0541s 5/7/05
-------+---------+---------+---------+-6.0
7.5
9.0
10.5
Pooled StDev = 1.606
Executing from file: 2522onme4.MTB
Executing from file: 2522osme4.MTB
Data Display
Row
1
2
3
4
5
C1
8.75
9.50
9.25
9.50
9.25
C2
9.5
4.0
5.5
8.5
4.5
Data Display
Row
1
2
3
4
5
x1sq
76.5625
90.2500
85.5625
90.2500
85.5625
C3
8.5
8.5
7.5
7.5
8.0
x2sq
90.25
16.00
30.25
72.25
20.25
C4
11.5
11.0
7.5
7.5
8.0
x3sq
72.25
72.25
56.25
56.25
64.00
x4sq
132.25
121.00
56.25
56.25
64.00
Data Display
sumx1
sumx2
sumx3
sumx4
n1
n2
n3
n4
smx1sq
smx2sq
smx3sq
smx4sq
46.2500
32.0000
40.0000
45.5000
5.00000
5.00000
5.00000
5.00000
428.188
229.000
321.000
429.750
Executing from file: 2522omea4.MTB
Data Display
x1bar
x2bar
x3bar
x4bar
9.25000
6.40000
8.00000
9.10000
Data Display
smxsq
n
sumx
srss
gdmn
srmsq
x1bsq
x2bsq
x3bsq
x4bsq
sxbsq
K26
SSR
SSC
SST
1407.94
20.0000
163.750
1407.94
8.18750
338.199
85.5625
40.9600
64.0000
82.8100
273.333
1340.70
12.0938
25.9594
67.2344
17
252y0541s 5/7/05
Data Display
Row
C1
1 8.75
2 9.50
3 9.25
4 9.50
5 9.25
Executing
Executing
Executing
Executing
Executing
C2
9.5
4.0
5.5
8.5
4.5
from
from
from
from
from
C3
8.5
8.5
7.5
7.5
8.0
file:
file:
file:
file:
file:
C4
rsum
11.5 38.25
11.0 33.00
7.5 29.75
7.5 33.00
8.0 29.75
2522wr1.MTB
2522wr1.MTB
2522wr1.MTB
2522wr1.MTB
252-2W1O.MTB
rmn
9.5625
8.2500
7.4375
8.2500
7.4375
rss
371.313
299.500
228.313
275.000
233.813
rmnsq
91.4414
68.0625
55.3164
68.0625
55.3164
Tabulated statistics: C41, C42
Rows: C41
Columns: C42
1 2 3 4 All
1
2
3
4
5
All
1
1
1
1
1
5
1
1
1
1
1
5
1
1
1
1
1
5
1
1
1
1
1
5
Cell Contents:
4
4
4
4
4
20
Count
Tabulated statistics: C41, C42
Rows: C41
1
1
8.75
2
9.50
3
9.25
4
9.50
5
9.25
Columns: C42
2
3
4
9.50 8.50 11.50
4.00 8.50 11.00
5.50 7.50
7.50
8.50 7.50
7.50
4.50 8.00
8.00
Cell Contents:
C40
:
DATA
Tabulated statistics: C41, C42
Rows: C41
1
2
3
4
5
All
Columns:
2
9.500
4.000
5.500
8.500
4.500
6.400
1
8.750
9.500
9.250
9.500
9.250
9.250
Cell Contents:
C40
C42
3
8.500
8.500
7.500
7.500
8.000
8.000
:
4
11.500
11.000
7.500
7.500
8.000
9.100
All
9.563
8.250
7.438
8.250
7.438
8.188
Mean
Two-way ANOVA: C40 versus C41, C42
Source
C41
C42
Error
Total
DF
4
3
12
19
S = 1.559
SS
12.0938
25.9594
29.1813
67.2344
MS
3.02344
8.65312
2.43177
R-Sq = 56.60%
F
1.24
3.56
P
0.344
0.048
R-Sq(adj) = 31.28%
18
252y0541s 5/7/05
Executing from file: 2522wfo4.MTB
Data Display
Row
1
2
3
4
5
6
7
8
9
10
C31
8.750
9.500
9.250
9.500
9.250
46.250
5.000
9.250
428.188
85.563
C32
9.50
4.00
5.50
8.50
4.50
32.00
5.00
6.40
229.00
40.96
C33
8.5
8.5
7.5
7.5
8.0
40.0
5.0
8.0
321.0
64.0
C38
11.50
11.00
7.50
7.50
8.00
45.50
5.00
9.10
429.75
82.81
C34
38.25
33.00
29.75
33.00
29.75
163.75
20.00
8.19
1407.94
273.33
C35
9.5625
8.2500
7.4375
8.2500
7.4375
8.1875
C36
371.31
299.50
228.31
275.00
233.81
1407.94
C37
91.441
68.063
55.316
68.063
55.316
338.199
Data Display
Row
1
2
3
4
SS.
12.0938
25.9594
29.1813
67.2344
DF.
4
3
12
19
MS.
3.02344
8.65312
2.43177
3.53865
F.
1.24331
3.55836
1.00000
1.45517
MTB >
19
252y0541s 5/7/05
Problem 5 - Chisquared
Effectiveness
Very Effective
Effective
Ineffective
Total
< 1 mo.
15
9
5
29
D u r a
1-2 mo.
28
26
2
56
t i o n
2-4 mo.
24
33
3
60
>4 mo.
6
19
5
30
Total
73
87
15
175
————— 5/5/2005 10:42:53 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05047.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-7.MTW'
Worksheet was saved on Fri Apr 29 2005
Results for: 252x0504-8.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05048.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-8.MTW'
MTB > let c14 = c10 + c11 + c12 +c13
MTB > sum c14
Sum of totO
Sum of totO = 175
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
>
>
>
>
>
>
>
>
>
>
>
let
let
let
let
let
let
let
let
let
let
let
c15=c14/175
k10= sum (c10)
c20 = c15* k10
k11 = sum (c11)
c21 = c15* k11
k12 = sum (c12)
c22 = k12 * c15
k13 = sum (c13)
c23 = k13 * c15
c24 = c20 + c21 + c22 + c23
k20 = sum c20
MTB
MTB
MTB
MTB
MTB
>
>
>
>
>
let k20 =
let k21 =
let k22 =
let k23 =
print k10
sum(c20)
sum(c21)
sum (c22)
sum (c23)
k21 k11 k21 k12 k22 k13 k23
Data Display
K10
K20
K11
K21
K12
K22
K13
K23
MTB
MTB
MTB
MTB
29.0000
29.0000
56.0000
56.0000
60.0000
60.0000
30.0000
30.0000
>
>
>
>
let
let
let
let
c30
c31
c30
c31
=
=
=
=
c20
c21
100 * c20
100 * c21
20
252y0541s 5/7/05
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
>
>
>
>
>
>
>
>
>
>
>
>
let c32 =
let c33 =
round c30
round c31
round c32
round c33
let c30 =
let c31 =
let c32 =
let c33 =
let c34 =
sum c30
100 * c22
100 * c23
c30
c31
c32
c33
c30/100
c31/100
c32/100
c33/100
c30 + c31+ c32 + c33
Sum of 1moE1
Sum of 1moE1 = 29.01
MTB > sum c31
Sum of 2moE1
Sum of 2moE1 = 56
MTB > sum c32
Sum of 4moE1
Sum of 4moE1 = 60
MTB > sum c33
Sum of momoE1
Sum of momoE1 = 29.99
MTB > print c10 - c14
Data Display
Row
1
2
3
1mo
15
9
5
2mo
28
26
2
4mo
24
33
3
momo
6
19
5
totO
73
87
15
MTB > print c10 - c15
Data Display
Row
1
2
3
1mo
15
9
5
2mo
28
26
2
4mo
24
33
3
momo
6
19
5
totO
73
87
15
pr
0.417143
0.497143
0.085714
MTB > print c20 - c24
Data Display
Row
1
2
3
1moE
12.0971
14.4171
2.4857
2moE
23.36
27.84
4.80
4moE
25.0286
29.8286
5.1429
momoE
12.5143
14.9143
2.5714
totE
73
87
15
MTB > print c30 - c34
Data Display
Row
1
2
3
1moE1
12.10
14.42
2.49
2moE1
23.36
27.84
4.80
4moE1
25.03
29.83
5.14
momoE1
12.51
14.91
2.57
C34
73
87
15
MTB > Stack c10 c11 c12 c13 c1.
MTB > stack c30 c31 c32 c33 c2.
MTB > sum c1
Sum of C1
Sum of C1 = 175
MTB > sum c2
21
252y0541s 5/7/05
Sum of C2
Sum of C2 = 175
MTB > exec '252chisq'
Executing from file: 252chisq.MTB
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
O
15
9
5
28
26
2
24
33
3
6
19
5
E
12.10
14.42
2.49
23.36
27.84
4.80
25.03
29.83
5.14
12.51
14.91
2.57
C3
-2.90
5.42
-2.51
-4.64
1.84
2.80
1.03
-3.17
2.14
6.51
-4.09
-2.43
C4
8.4100
29.3764
6.3001
21.5296
3.3856
7.8400
1.0609
10.0489
4.5796
42.3801
16.7281
5.9049
C5
0.69504
2.03720
2.53016
0.92164
0.12161
1.63333
0.04239
0.33687
0.89097
3.38770
1.12194
2.29763
C6
18.5950
5.6172
10.0402
33.5616
24.2816
0.8333
23.0124
36.5069
1.7510
2.8777
24.2119
9.7276
O-Esq
8.4100
29.3764
6.3001
21.5296
3.3856
7.8400
1.0609
10.0489
4.5796
42.3801
16.7281
5.9049
O-esq/E
0.69504
2.03720
2.53016
0.92164
0.12161
1.63333
0.04239
0.33687
0.89097
3.38770
1.12194
2.29763
Osq/E
18.5950
5.6172
10.0402
33.5616
24.2816
0.8333
23.0124
36.5069
1.7510
2.8777
24.2119
9.7276
Data Display
n
175.000
K2
175.000
K3
-0.000000000
chisq1
16.0165
chisq
16.0165
K6
191.016
MTB > print c1-c6
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
O
15
9
5
28
26
2
24
33
3
6
19
5
E
12.10
14.42
2.49
23.36
27.84
4.80
25.03
29.83
5.14
12.51
14.91
2.57
O-E
-2.90
5.42
-2.51
-4.64
1.84
2.80
1.03
-3.17
2.14
6.51
-4.09
-2.43
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x05048.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-8.MTW'
Existing file replaced.
22
252y0541s 5/7/05
Problem 5 - 2 proportions.
————— 5/6/2005 1:14:09 AM ————————————————————
Welcome to Minitab, press F1 for help.
Results for: 252x0504-8a.MTW
MTB > erase k1 -k200
MTB > erase c1-c100
MTB > exec '252-2p1'
Executing from file: 252-2p1.MTB
Executing from file: 252-2prp.MTB
Data Display
x1
n1
p1
x2
n2
p2
7.00000
65.0000
0.107692
8.00000
90.0000
0.0888889
Data Display
p0
n
sdp2
q0
q1
q2
K213
K214
K215
sdp1
K217
K218
0.0967742
155.000
0.0487672
0.903226
0.892308
0.911111
0.00147838
0.000899863
0.00231596
0.0481245
0.0188034
0.00237824
Data Display
1 poold
0
delp
0.0188034
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x05048a.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-8a.MTW'
Existing file replaced.
MTB >
23
252y0541s 5/7/05
Problem 5 - Poisson problem
e) (Anderson et. al.) The number of emergency calls our Fire department receives is believed to
have a Poisson distribution with a parameter of 3. Test this against data for a period of 120 days: 0
calls on 9 days, 1 call on 12 days, 2 calls on 30 days, 3 calls on 27 days, 4 calls on 22 days. 5 calls
on 13 days and 7 calls on 6 days. (5)
This is the Poisson 3 table.
k P(x=k)
P(xk)
0 0.049787 0.04979
1 0.149361 0.19915
2 0.224042 0.42319
3 0.224042 0.64723
4 0.168031 0.81526
5 0.100819 0.91608
6 0.050409 0.96649
7 0.021604 0.98810
8 0.008102 0.99620
9 0.002701 0.99890
10 0.000810 0.99971
11 0.000221 0.99993
12 0.000055 0.99998
13 0.000013 1.00000
14 0.000003 1.00000
15 0.000001 1.00000
16 0.000000 1.00000
17 0.000000 1.00000
P(x=k)
0.049787
0.149361
0.224042
0.224042
0.168031
0.100819
0.050409
0.021604
0.008102
0.002701
0.000810
0.000221
0.000055
0.000013
0.000003
0.000001
0.000000
0.000000
P(xk)
0.04979
0.19915
0.42319
0.64723
0.81526
0.91608
0.96649
0.98810
0.99620
0.99890
0.99971
0.99993
0.99998
1.00000
1.00000
1.00000
1.00000
1.00000
————— 5/6/2005 1:14:09 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05048b.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-8b.MTW'
Worksheet was saved on Fri May 06 2005
Results for: 252x0504-8b1.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05048b1.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-8b1.MTW'
MTB > let c1 = c10
MTB > let c2 = c11
MTB > exec '252chisq'
Executing from file: 252chisq.MTB
24
252y0541s 5/7/05
Data Display
Row
1
2
3
4
5
6
7
O
9
12
30
27
22
13
7
E
5.9744
17.9233
26.8850
26.8850
20.1637
12.0983
10.0704
C3
-3.02556
5.92332
-3.11496
-0.11496
-1.83628
-0.90172
3.07040
C4
9.1540
35.0857
9.7030
0.0132
3.3719
0.8131
9.4274
C5
1.53220
1.95755
0.36091
0.00049
0.16723
0.06721
0.93615
E1
5.9744
17.9233
26.8850
26.8850
20.1637
12.0983
6.0491
2.5925
0.9722
0.3241
0.0972
0.0265
0.0066
0.0016
0.0004
0.0001
0.0000
0.0000
Fcum
0.04979
0.19915
0.42319
0.64723
0.81526
0.91608
0.96649
0.98810
0.99620
0.99890
0.99971
0.99993
0.99998
1.00000
1.00000
1.00000
1.00000
1.00000
C6
13.5578
8.0342
33.4759
27.1155
24.0035
13.9689
4.8657
Data Display
n
K2
K3
chisq1
chisq
K6
120.000
120.000
0.000240000
5.02148
5.02172
125.021
MTB > print c10-c14
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
O1
9
12
30
27
22
13
7
E2
5.9744
17.9233
26.8850
26.8850
20.1637
12.0983
10.0704
f
0.049787
0.149361
0.224042
0.224042
0.168031
0.100819
0.050409
0.021604
0.008102
0.002701
0.000810
0.000221
0.000055
0.000013
0.000003
0.000001
0.000000
0.000000
————— 5/6/2005 1:14:07 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05048b2.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-8b2.MTW'
Worksheet was saved on Fri May 06 2005
Results for: 252x0504-8b2.MTW
MTB > exec '252KSO'
Executing from file: 252KSO.MTB
Executing from file: 252ksc.MTB
25
252y0541s 5/7/05
Data Display
Row
1
2
3
4
5
6
7
O
9
12
30
27
22
13
7
O/n
0.075000
0.100000
0.250000
0.225000
0.183333
0.108333
0.058333
FO
0.07500
0.17500
0.42500
0.65000
0.83333
0.94167
1.00000
Data Display
n
120.000
MTB > exec '252ks'
Executing from file: 252ks.MTB
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
FE
0.04979
0.19915
0.42319
0.64723
0.81526
0.91608
0.96649
0.98810
0.99620
0.99890
0.99971
0.99993
0.99998
1.00000
1.00000
1.00000
1.00000
1.00000
D
0.0252100
0.0241500
0.0018100
0.0027700
0.0180733
0.0255867
0.0335100
0.0119000
0.0038000
0.0011000
0.0002900
0.0000700
0.0000200
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
Data Display
max D
0.0335100
MTB > print c1 c6 c3 c4 c5
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
O
9
12
30
27
22
13
7
O/n
0.075000
0.100000
0.250000
0.225000
0.183333
0.108333
0.058333
FO
0.07500
0.17500
0.42500
0.65000
0.83333
0.94167
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
FE
0.04979
0.19915
0.42319
0.64723
0.81526
0.91608
0.96649
0.98810
0.99620
0.99890
0.99971
0.99993
0.99998
1.00000
1.00000
1.00000
1.00000
1.00000
D
0.0252100
0.0241500
0.0018100
0.0027700
0.0180733
0.0255867
0.0335100
0.0119000
0.0038000
0.0011000
0.0002900
0.0000700
0.0000200
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
MTB >
26
252y0541s 5/7/05
Problem 6
————— 4/29/2005 4:38:10 AM ————————————————————
Welcome to Minitab, press F1 for help.
Results for: 252x0504-7.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05047.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-7.MTW'
MTB > let d = c2-c3
MTB > sum c2
Sum of 2001
Sum of 2001 = 2860.46
MTB > ssq c2
Sum of Squares of 2001
Sum of squares (uncorrected) of 2001 = 953941
MTB > sum c3
Sum of 2002
Sum of 2002 = 2954.56
MTB > ssq c3
Sum of Squares of 2002
Sum of squares (uncorrected) of 2002 = 999629
MTB > sum c4
Sum of d
Sum of d = -94.104
MTB > ssq c4
Sum of Squares of d
Sum of squares (uncorrected) of d = 3724.97
MTB > print c1-c4
Data Display
Row
1
2
3
4
5
6
7
8
9
10
Location
Alexandria
Boston
Decatur
Kirkland
New York
Philadephia
Phoenix
Raleigh
San Bruno
Tampa
2001
245.795
391.750
205.270
326.524
545.363
185.736
170.413
210.015
385.387
194.205
2002
293.266
408.803
227.561
333.569
531.098
197.874
175.030
196.094
391.409
199.858
d
-47.471
-17.053
-22.291
-7.045
14.265
-12.138
-4.617
13.921
-6.022
-5.653
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x05047.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-7.MTW'
Existing file replaced.
MTB >
————— 5/6/2005 6:05:38 AM ————————————————————
27
252y0541s 5/7/05
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05047.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-7.MTW'
Worksheet was saved on Fri Apr 29 2005
Results for: 252x0504-7.MTW
MTB > Rank 'd' c5.
MTB > print c1-c5
Data Display
Row
1
2
3
4
5
6
7
8
9
10
MTB
MTB
MTB
MTB
Location
2001
2002
Alexandria
245.795 293.266
Boston
391.750 408.803
Decatur
205.270 227.561
Kirkland
326.524 333.569
New York
545.363 531.098
Philadephia 185.736 197.874
Phoenix
170.413 175.030
Raleigh
210.015 196.094
San Bruno
385.387 391.409
Tampa
194.205 199.858
> let c6 = c4
> let c5 = absolute(c4)
> rank c5 c6
> print c1-c6
Data Display
Row
1
2
3
4
5
6
7
8
9
10
Location
Alexandria
Boston
Decatur
Kirkland
New York
Philadephia
Phoenix
Raleigh
San Bruno
Tampa
MTB >
SUBC>
SUBC>
MTB >
MTB >
SUBC>
SUBC>
SUBC>
MTB >
2001
245.795
391.750
205.270
326.524
545.363
185.736
170.413
210.015
385.387
194.205
2002
293.266
408.803
227.561
333.569
531.098
197.874
175.030
196.094
391.409
199.858
d
-47.471
-17.053
-22.291
-7.045
14.265
-12.138
-4.617
13.921
-6.022
-5.653
C5
1
3
2
5
10
4
8
9
6
7
d
-47.471
-17.053
-22.291
-7.045
14.265
-12.138
-4.617
13.921
-6.022
-5.653
C5
47.471
17.053
22.291
7.045
14.265
12.138
4.617
13.921
6.022
5.653
C6
10
8
9
4
7
5
1
6
3
2
Stack c2 c3 c10;
Subscripts c11;
UseNames.
Rank c10 c12.
Unstack (c12);
Subscripts c11;
After;
VarNames.
print c1 c2 c13 c3 c14
28
252y0541s 5/7/05
Data Display
Row
1
2
3
4
5
6
7
8
9
10
Location
Alexandria
Boston
Decatur
Kirkland
New York
Philadephia
Phoenix
Raleigh
San Bruno
Tampa
2001
245.795
391.750
205.270
326.524
545.363
185.736
170.413
210.015
385.387
194.205
C12_2001
11
17
8
13
20
3
1
9
15
4
2002
293.266
408.803
227.561
333.569
531.098
197.874
175.030
196.094
391.409
199.858
C12_2002
12
18
10
14
19
6
2
5
16
7
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x05047.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-7.MTW'
Existing file replaced.
MTB >
29
252y0541s 5/7/05
Part III
252x0541 4/22/05
ECO252 QBA2
Final EXAM
May 2-6, 2004
TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
Class days and time : _________________________
Please Note: computer problems 2,3 and 4 should be turned in with the exam (2). In problem 2, the 2 way
ANOVA table should be checked. The three F tests should be done with a 5% significance level and you
should note whether there was (i) a significant difference between drivers, (ii) a significant difference
between cars and (iii) significant interaction. In problem 3, you should show on your third graph where the
regression line is. Check what your text says about normal probability plots and analize the plot you did.
Explain the results of the t and F tests using a 5% significance level. (2)
4th computer problem (4+)
This is an internet project. You are trying to answer the question, ‘how well does manufacturing explain
differences in income?’ You should use some measure of income per person or family in each state as your
dependent variable and try to explain it as a function of (to start with) percent of output or labor force in
manufacturing. This should start out as a simple regression. Then you should try to see whether there are
other variables that explain the differences as well. One possibility is the per cent of the adult population
with college or high school diplomas. Possible sources of data are below, but think about what you use, and
try to find some other sources. Total income of a state, for example is a very poor choice, rather than some
per capita measure because it is simply going to be high for places with a lot of people without indicating
how well off they are. 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.
http://www.nam.org/s_nam/sec.asp?CID=5&DID=3 Manufacturing share in state economies
(http://www.nam.org/Docs/IEA/26767_20002001ManufacturingShareandChangeinStateEconomies.pdf?DocTypeID=9&TrackID=&Param=@CategoryI
D=1156@TPT=2002-2001+Manufacturing+Share+and+Change+in+State+Economics)
http://www.nemw.org/data.htm Per capita income by state.
http://www.nemw.org/data.htm State personal income per capita.
http://www.bea.doc.gov/bea/regional/data.htm Personal income per capita by state.
http://www.census.gov/statab/www/ Many state statistics, including persons with bachelor’s degrees.
http://www.epinet.org/content.cfm/datazone_index Income inequality, median income, unemployment rates.
Anyway, your job is to add whatever variable you think ought to explain your income measure. Consider all
50 states your sample. Your report should tell what numbers you used, from where and from what years.
What coefficients were significant and do you think on the basis of your results that manufacturing is an
important predictor of a state’s prosperity? Mark all significant F and t coefficients using a 5% significance
level. Explain VIFs.
Of course, if you don’t like this assignment, get approval to research something else on the internet. For
example, does the per cent of the population in prison affect the crime rate (maybe with a few years’ lag)?
Or are there better predictors? And get out the Durbin-Watson, prison vs. crime rate is a time series project.
[8]
30
252y0541s 5/7/05
old
x1
y
Row
INC
1 39.0
2 43.7
3 62.6
4 42.8
5 55.0
6 60.6
7 59.4
8 57.1
9 56.5
10 53.5
11 55.7
12 58.8
13 64.1
14 58.8
15 62.5
16 60.0
17 72.9
18 56.1
19 67.1
20 82.3
1168.5
EDUC
2
4
8
8
8
10
12
12
12
12
12
13
14
14
15
15
16
16
17
21
241
x2
x12
x 22
SEX
0
4
1
16
0
64
1
64
0
64
0
100
0
144
0
144
0
144
1
144
1
144
0
169
0
196
1
196
0
225
1
225
0
256
1
256
0
289
0
441
7 3285
y2
x1 y
x2 y
0 1521.00
78.0
0.0
1 1909.69
174.8 43.7
0 3918.76
500.8
0.0
1 1831.84
342.4 42.8
0 3025.00
440.0
0.0
0 3672.36
606.0
0.0
0 3528.36
712.8
0.0
0 3260.41
685.2
0.0
0 3192.25
678.0
0.0
1 2862.25
642.0 53.5
1 3102.49
668.4 55.7
0 3457.44
764.4
0.0
0 4108.81
897.4
0.0
1 3457.44
823.2 58.8
0 3906.25
937.5
0.0
1 3600.00
900.0 60.0
0 5314.41 1166.4
0.0
1 3147.21
897.6 56.1
0 4502.41 1140.7
0.0
0 6773.29 1728.3
0.0
7 70091.67 14783.9 370.6
x1 x 2
0
4
0
8
0
0
0
0
0
12
12
0
0
14
0
15
0
16
0
0
81
Part III Original Regression
————— 4/22/2005 12:30:46 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05042.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-2.MTW'
Worksheet was saved on Fri Apr 22 2005
Results for: 252x0504-2.MTW
MTB > echo
MTB > Execute "C:\Documents and Settings\rbove\My Documents\Minitab\252OLS2.mtb"
1.
Executing from file: C:\Documents and Settings\rbove\My
Documents\Minitab\252OLS2.mtb
MTB > #252OLS2 #Does spare parts for a regression problem with 2 #independent #v
> ariables. Put y in C1, x1 in C2, x2 in #c3.
MTB > Regress c1 1 c2
Regression Analysis: INC versus EDUC
The regression equation is
INC = 36.2 + 1.85 EDUC
Predictor
Constant
EDUC
S = 5.39031
Coef
36.173
1.8466
SE Coef
3.539
0.2762
R-Sq = 71.3%
T
10.22
6.69
P
0.000
0.000
R-Sq(adj) = 69.7%
31
252y0541s 5/7/05
old
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
18
19
SS
1299.1
523.0
1822.1
MS
1299.1
29.1
F
44.71
P
0.000
Unusual Observations
Obs
1
3
EDUC
2.0
8.0
INC
39.00
62.60
Fit
39.87
50.95
SE Fit
3.03
1.64
Residual
-0.87
11.65
St Resid
-0.19 X
2.27R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > Regress c1 2 c2 c3
Regression Analysis: INC versus EDUC, SEX
The regression equation is
INC = 39.4 + 1.78 EDUC - 7.12 SEX
Predictor
Constant
EDUC
SEX
Coef
39.420
1.7840
-7.121
S = 4.15717
SE Coef
2.872
0.2137
1.955
R-Sq = 83.9%
T
13.73
8.35
-3.64
P
0.000
0.000
0.002
R-Sq(adj) = 82.0%
Analysis of Variance
Source
Regression
Residual Error
Total
Source
EDUC
SEX
DF
1
1
DF
2
17
19
SS
1528.26
293.79
1822.06
MS
764.13
17.28
F
44.22
P
0.000
Seq SS
1299.06
229.20
Unusual Observations
Obs
3
EDUC
8.0
INC
62.600
Fit
53.692
SE Fit
1.475
Residual
8.908
St Resid
2.29R
R denotes an observation with a large standardized residual.
MTB > execute '252OLS2namer' #Names Columns and Constants.
Executing from file: 252OLS2namer.MTB
MTB > #252OLS2namer Names columns and constants
MTB > #Part of 252OLS2
MTB > name c5 'x1sq'
MTB > name c6 'x2sq'
MTB > name c7 'ysq'
MTB > name c8 'x1y'
MTB > name c9 'x2y'
MTB > name c10 'x1x2'
MTB > name k1 'sumy'
32
252y0541s 5/7/05
Old
MTB > name k2 'sumx1'
MTB > name k3 'sumx2'
MTB > name k4 'n'
MTB > name k5 'smx1sq'
MTB > name k6 'smx2sq'
MTB > name k7 'smysq'
MTB > name k8 'smx1y'
MTB > name k9 'smx2y'
MTB > name k10 'smx1x2'
MTB > name k11 'ybar'
MTB > name k12 'x1bar'
MTB > name k13 'x2bar'
MTB > name k15 'SSx1'
MTB > name k16 'SSx2'
MTB > name k17 'SSy'
MTB > name k18 'Sx1y'
MTB > name k19 'Sx2y'
MTB > name k20 'Sx1x2'
MTB > end
MTB > execute '252OLS2sumer' #Sums Columns.
Executing from file: 252OLS2sumer.MTB
MTB > #252OLS2sumer Fills columns and sums them
MTB > #Part of 252OLS2
MTB > let k1=sum(c1) #Sum of y
MTB > let k2=sum(c2) #Sum of x1
MTB > let k3=sum(c3) #Sum of x2
MTB > let k4=count(c1) #n
MTB > let c5=c2*c2
MTB > let k5= sum(c5) #Sum of x1 squared
MTB > let c6=c3*c3
MTB > let k6=sum(c6) #Sum of x2 squared
MTB > let c7=c1*c1
MTB > let k7= sum(c7) #Sum of y squared
MTB > let c8=c2*c1
MTB > let k8=sum(c8) #Sum of x1*y
MTB > let c9=c3*c1
MTB > let k9=sum(c9) #Sum of x2*y
MTB > let c10=c2*c3
MTB > let k10=sum(c10) #Sum of x1*x2
MTB > end
MTB > print c1-c5
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
INC
39.0
43.7
62.6
42.8
55.0
60.6
59.4
57.1
56.5
53.5
55.7
58.8
64.1
58.8
62.5
60.0
72.9
56.1
67.1
82.3
EDUC
2
4
8
8
8
10
12
12
12
12
12
13
14
14
15
15
16
16
17
21
SEX
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
C4
x1sq
4
16
64
64
64
100
144
144
144
144
144
169
196
196
225
225
256
256
289
441
33
252y0541s 5/7/05
* NOTE * One or more variables are undefined.
MTB > print c6-c10
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
x2sq
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
ysq
1521.00
1909.69
3918.76
1831.84
3025.00
3672.36
3528.36
3260.41
3192.25
2862.25
3102.49
3457.44
4108.81
3457.44
3906.25
3600.00
5314.41
3147.21
4502.41
6773.29
x1y
78.0
174.8
500.8
342.4
440.0
606.0
712.8
685.2
678.0
642.0
668.4
764.4
897.4
823.2
937.5
900.0
1166.4
897.6
1140.7
1728.3
x2y
0.0
43.7
0.0
42.8
0.0
0.0
0.0
0.0
0.0
53.5
55.7
0.0
0.0
58.8
0.0
60.0
0.0
56.1
0.0
0.0
x1x2
0
4
0
8
0
0
0
0
0
12
12
0
0
14
0
15
0
16
0
0
MTB > print k1-k10
Data Display
sumy
sumx1
sumx2
n
smx1sq
smx2sq
smysq
smx1y
smx2y
smx1x2
1168.50
241.000
7.00000
20.0000
3285.00
7.00000
70091.7
14783.9
370.600
81.0000
MTB > execute '252OLS2mean' #Computes means.
Executing from file: 252OLS2mean.MTB
MTB > #252OLS2mean Computes means
MTB > #Part of 252OLS2
MTB > let k11=k1/k4 #Mean of y
MTB > let k12=k2/k4 #Mean of x1
MTB > let k13=k3/k4 #Mean of x2
MTB > end
MTB > print k11-k13
Data Display
ybar
x1bar
x2bar
58.4250
12.0500
0.350000
MTB > execute '252OLS2ss' #Computes spare parts.
Executing from file: 252OLS2ss.MTB
MTB > #252OLS2ss Computes spare parts
MTB > #Part of 252OLS2
MTB > let k15=k4*k12*k12
34
252y0541s 5/7/05
Old
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
>
>
>
>
>
>
>
>
>
>
>
>
>
let k15=k5-k15 #SSx1
let k16=k4*k13*k13
let k16=k6-k16 #SSx2
let k17=k4*k11*k11
let k17=k7-k17 #SSy
let k18=k4*k12*k11
let k18=k8-k18 #Sx1y
let k19=k4*k13*k11
let k19=k9-k19 #Sx2y
let k20=k4*k12*k13
let k20=k10-k20 #Sx1x2
end
print k15-k20
Data Display
SSx1
SSx2
SSy
Sx1y
Sx2y
Sx1x2
380.950
4.55000
1822.06
703.475
-38.3750
-3.35000
MTB > end
MTB >
MTB > print c1 c2 c3 c5 c6 c7 c8 c9 c10
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
INC
39.0
43.7
62.6
42.8
55.0
60.6
59.4
57.1
56.5
53.5
55.7
58.8
64.1
58.8
62.5
60.0
72.9
56.1
67.1
82.3
EDUC
2
4
8
8
8
10
12
12
12
12
12
13
14
14
15
15
16
16
17
21
SEX
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
x1sq
4
16
64
64
64
100
144
144
144
144
144
169
196
196
225
225
256
256
289
441
x2sq
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
ysq
1521.00
1909.69
3918.76
1831.84
3025.00
3672.36
3528.36
3260.41
3192.25
2862.25
3102.49
3457.44
4108.81
3457.44
3906.25
3600.00
5314.41
3147.21
4502.41
6773.29
x1y
78.0
174.8
500.8
342.4
440.0
606.0
712.8
685.2
678.0
642.0
668.4
764.4
897.4
823.2
937.5
900.0
1166.4
897.6
1140.7
1728.3
x2y
0.0
43.7
0.0
42.8
0.0
0.0
0.0
0.0
0.0
53.5
55.7
0.0
0.0
58.8
0.0
60.0
0.0
56.1
0.0
0.0
x1x2
0
4
0
8
0
0
0
0
0
12
12
0
0
14
0
15
0
16
0
0
MTB >
35
252y0541s 5/7/05
Part III Modified Regression
————— 5/6/2005 7:06:37 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05041.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-1.MTW'
Worksheet was saved on Thu Apr 21 2005
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-2.MTW'
Worksheet was saved on Fri Apr 22 2005
Results for: 252x0504-2a.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05042a.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-2a.MTW'
MTB > Execute "C:\Documents and Settings\rbove\My Documents\Minitab\252OLS2.mtb"
1.
Executing from file: C:\Documents and Settings\rbove\My
Documents\Minitab\252OLS2.mtb
Regression Analysis: INC versus EDUC
The regression equation is
INC = 38.7 + 1.84 EDUC
Predictor
Constant
EDUC
Coef
38.657
1.8403
S = 12.4779
SE Coef
8.169
0.6393
R-Sq = 30.4%
T
4.73
2.88
P
0.000
0.010
R-Sq(adj) = 26.7%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
19
20
SS
1290.2
2958.3
4248.5
Unusual Observations
Obs EDUC
INC
Fit
1
2.0
39.00 42.34
21 12.0 108.90 60.74
MS
1290.2
155.7
SE Fit
6.98
2.72
F
8.29
P
0.010
Residual
-3.34
48.16
St Resid
-0.32 X
3.95R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
Regression Analysis: INC versus EDUC, SEX
The regression equation is
INC = 38.7 + 1.84 EDUC - 0.18 SEX
Predictor
Constant
EDUC
SEX
Coef
38.747
1.8387
-0.184
S = 12.8195
SE Coef
8.854
0.6588
5.778
R-Sq = 30.4%
T
4.38
2.79
-0.03
P
0.000
0.012
0.975
R-Sq(adj) = 22.6%
36
252y0541s 5/7/05
Analysis of Variance
Source
Regression
Residual Error
Total
Source
EDUC
SEX
DF
1
1
DF
2
18
20
SS
1290.4
2958.1
4248.5
MS
645.2
164.3
F
3.93
P
0.038
Seq SS
1290.2
0.2
Unusual Observations
Obs EDUC
INC
Fit
21 12.0 108.90 60.63
SE Fit
4.54
Residual
48.27
St Resid
4.03R
R denotes an observation with a large standardized residual.
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
17
18
19
20
21
INC
39.0
43.7
62.6
42.8
55.0
60.6
59.4
57.1
56.5
53.5
55.7
58.8
64.1
58.8
62.5
60.0
72.9
56.1
67.1
82.3
108.9
EDUC
2
4
8
8
8
10
12
12
12
12
12
13
14
14
15
15
16
16
17
21
12
SEX
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
C4
x1sq
4
16
64
64
64
100
144
144
144
144
144
169
196
196
225
225
256
256
289
441
144
* NOTE * One or more variables are undefined.
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
x2sq
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
ysq
1521.0
1909.7
3918.8
1831.8
3025.0
3672.4
3528.4
3260.4
3192.3
2862.3
3102.5
3457.4
4108.8
3457.4
3906.3
3600.0
5314.4
x1y
78.0
174.8
500.8
342.4
440.0
606.0
712.8
685.2
678.0
642.0
668.4
764.4
897.4
823.2
937.5
900.0
1166.4
x2y
0.0
43.7
0.0
42.8
0.0
0.0
0.0
0.0
0.0
53.5
55.7
0.0
0.0
58.8
0.0
60.0
0.0
x1x2
0
4
0
8
0
0
0
0
0
12
12
0
0
14
0
15
0
37
252y0541s 5/7/05
18
19
20
21
1
0
0
1
3147.2
4502.4
6773.3
11859.2
897.6
1140.7
1728.3
1306.8
56.1
0.0
0.0
108.9
16
0
0
12
Data Display
sumy
sumx1
sumx2
n
smx1sq
smx2sq
smysq
smx1y
smx2y
smx1x2
1277.40
253.000
8.00000
21.0000
3429.00
8.00000
81950.9
16090.7
479.500
93.0000
Executing from file: 252OLS2mean.MTB
Data Display
ybar
x1bar
x2bar
60.8286
12.0476
0.380952
Executing from file: 252OLS2ss.MTB
Data Display
SSx1
SSx2
SSy
Sx1y
Sx2y
Sx1x2
380.952
4.95238
4248.46
701.071
-7.12857
-3.38095
MTB >
MTB > print c1 c2 c3 c5 c6 c7 c8 c9 c10
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
INC
39.0
43.7
62.6
42.8
55.0
60.6
59.4
57.1
56.5
53.5
55.7
58.8
64.1
58.8
62.5
60.0
72.9
56.1
67.1
82.3
108.9
EDUC
2
4
8
8
8
10
12
12
12
12
12
13
14
14
15
15
16
16
17
21
12
SEX
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
x1sq
4
16
64
64
64
100
144
144
144
144
144
169
196
196
225
225
256
256
289
441
144
x2sq
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
ysq
1521.0
1909.7
3918.8
1831.8
3025.0
3672.4
3528.4
3260.4
3192.3
2862.3
3102.5
3457.4
4108.8
3457.4
3906.3
3600.0
5314.4
3147.2
4502.4
6773.3
11859.2
x1y
78.0
174.8
500.8
342.4
440.0
606.0
712.8
685.2
678.0
642.0
668.4
764.4
897.4
823.2
937.5
900.0
1166.4
897.6
1140.7
1728.3
1306.8
x2y
0.0
43.7
0.0
42.8
0.0
0.0
0.0
0.0
0.0
53.5
55.7
0.0
0.0
58.8
0.0
60.0
0.0
56.1
0.0
0.0
108.9
x1x2
0
4
0
8
0
0
0
0
0
12
12
0
0
14
0
15
0
16
0
0
12
MTB >
38
252y0541s 5/7/05
Kruskall – Wallis Problem
————— 4/22/2005 1:58:53 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05042.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-2.MTW'
Worksheet was saved on Fri Apr 22 2005
Results for: 252x0504-3.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05043.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-3.MTW'
MTB > erase c1-c10
MTB > describe c1-c3
Descriptive Statistics: A, B, C
Variable
A
B
C
N
7
6
7
N*
0
0
0
Mean
86.29
73.00
75.86
SE Mean
3.15
2.78
4.38
StDev
8.34
6.81
11.58
Minimum
70.00
65.00
60.00
Q1
82.00
65.75
61.00
Median
88.00
73.00
79.00
Q3
91.00
79.75
85.00
Maximum
96.00
82.00
88.00
MTB > Stack c1 c2 c3 c7;
SUBC>
Subscripts c8;
SUBC>
UseNames.
MTB > Kruskal-Wallis c7 c8.
Kruskal-Wallis Test: C7 versus C8
Kruskal-Wallis Test on C7
C8
A
B
C
Overall
N
8
7
8
23
H = 8.43
H = 8.48
Median
88.00
73.00
79.00
DF = 2
DF = 2
Ave Rank
17.4
7.7
10.3
12.0
P = 0.015
P = 0.014
Z
2.81
-2.00
-0.87
(adjusted for ties)
MTB > AOVOneway c1 c2 c3.
One-way ANOVA: A, B, C
Source
Factor
Error
Total
DF
2
20
22
S = 8.560
Level
A
B
C
N
8
7
8
SS
761.8
1465.5
2227.3
MS
380.9
73.3
R-Sq = 34.20%
Mean
86.500
73.000
76.250
StDev
7.746
6.218
10.780
F
5.20
P
0.015
R-Sq(adj) = 27.62%
Individual 95% CIs For Mean Based on
Pooled StDev
-----+---------+---------+---------+---(--------*--------)
(--------*---------)
(--------*--------)
-----+---------+---------+---------+---70.0
77.0
84.0
91.0
39
252y0541s 5/7/05
Pooled StDev = 8.560
MTB >
MTB > print c1-c3
Data Display
Row
1
2
3
4
5
6
7
8
A
96
82
88
70
90
91
87
88
B
65
74
72
66
79
82
73
C
60
73
85
61
79
85
88
79
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x05043.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-3.MTW'
Existing file replaced.
MTB >
MTB > sum c1
Sum of A
Sum of A = 692
MTB > ssq c1
Sum of Squares of A
Sum of squares (uncorrected) of A = 60278
MTB > sum c2
Sum of B
Sum of B = 511
MTB > ssq c2
Sum of Squares of B
Sum of squares (uncorrected) of B = 37535
MTB > Vartest c7 c8;
SUBC>
Confidence 95.0.
Test for Equal Variances: C7 versus C8
95% Bonferroni confidence intervals for standard deviations
C8
A
B
C
N
8
7
8
Lower
4.70735
3.66497
6.55135
StDev
7.7460
6.2183
10.7803
Upper
18.9708
16.8724
26.4022
Bartlett's Test (normal distribution)
Test statistic = 1.88, p-value = 0.391
Levene's Test (any continuous distribution)
Test statistic = 0.82, p-value = 0.453
Test for Equal Variances: C7 versus C8
MTB > NormTest 'A' ;
SUBC>
KSTest.
40
252y0541s 5/7/05
Probability Plot of A
MTB > NormTest 'B';
SUBC>
KSTest.
Probability Plot of B
MTB > NormTest 'C';
SUBC> KSTest.
Probability Plot of C
MTB >
Test for Equal Variances for C7
Probability Plot of A
Normal
Bartlett's Test
Test Statistic
P-Value
A
99
1. 88
0.391
Mean
86.5
StDev 7.746
N
8
KS
0.276
P-Value 0.073
Levene's Test
0. 82
0.453
90
Percent
C8
Test Statistic
P-Value
B
50
10
C
5
10
15
20
1
25
70
80
90
95% Bonferroni Confidence Intervals for StDevs
Probability Plot of B
Probability Plot of C
Normal
Normal
99
50
10
Mean
76.25
StDev
10.78
N
8
KS
0.171
P-Value >0.150
90
Percent
Percent
99
Mean
73
StDev
6.218
N
7
KS
0.156
P-Value >0.150
90
1
100
A
50
10
60
70
80
B
90
1
60
72
84
96
108
C
41
252y0541s 5/7/05
Kruskall – Wallis Problem – Modified Data
————— 5/7/2005 12:04:57 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05043.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-3.MTW'
Worksheet was saved on Fri Apr 22 2005
Results for: 252x0504-3a.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05043a.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0504-3a.MTW'
MTB > describe c1-c3
Descriptive Statistics: A, B, C
Variable
A
B
C
MTB >
SUBC>
SUBC>
MTB >
N
8
7
9
N*
0
0
0
Mean
86.50
73.00
70.33
SE Mean
2.74
2.35
6.80
StDev
7.75
6.22
20.41
Minimum
70.00
65.00
23.00
Q1
83.25
66.00
60.50
Median
88.00
73.00
79.00
Q3
90.75
79.00
85.00
Maximum
96.00
82.00
88.00
stack c1 c2 c3 c7;
subscripts c8;
usenames.
Kruskal-Wallis C7 c8
Kruskal-Wallis Test: C7 versus C8
Kruskal-Wallis Test on C7
C8
A
B
C
Overall
H = 8.63
H = 8.67
MTB >
MTB >
SUBC>
SUBC>
SUBC>
MTB >
MTB >
MTB >
SUBC>
SUBC>
SUBC>
MTB >
N
8
7
9
24
DF = 2
DF = 2
Ave Rank
18.4
8.7
10.2
12.5
P = 0.013
P = 0.013
Z
2.91
-1.68
-1.25
(adjusted for ties)
rank c11 c13
Unstack (c13);
Subscripts c12;
After;
VarNames.
rank c7 c9
erase c11-c16
Unstack (c9);
Subscripts c8;
After;
VarNames.
print c1 c10 c2 c11 c3 c12
Data Display
Row
1
2
3
4
5
6
7
8
9
Median
88.00
73.00
79.00
A
96
82
88
70
90
91
87
88
C9_A
24.0
14.5
20.0
6.0
22.0
23.0
18.0
20.0
B
65
74
72
66
79
82
73
C9_B
4.0
10.0
7.0
5.0
12.0
14.5
8.5
C
60
73
85
61
79
85
88
79
23
C9_C
2.0
8.5
16.5
3.0
12.0
16.5
20.0
12.0
1.0
42
252y0541s 5/7/05
MTB > sum c10
Sum of C9_A
Sum of C9_A = 147.5
MTB > sum c11
Sum of C9_B
Sum of C9_B = 61
MTB > sum c12
Sum of C9_C
Sum of C9_C = 91.5
MTB > Execute "C:\Documents and Settings\rbove\My
Documents\Minitab\252aov1w3.mtb" 1.
Executing from file: C:\Documents and Settings\rbove\My
Documents\Minitab\252aov1w3.mtb
One-way ANOVA: A, B, C
Source
Factor
Error
Total
DF
2
21
23
SS
1228
3986
5214
S = 13.78
Level
A
B
C
N
8
7
9
MS
614
190
F
3.23
R-Sq = 23.55%
Mean
86.50
73.00
70.33
StDev
7.75
6.22
20.41
P
0.060
R-Sq(adj) = 16.27%
Individual 95% CIs For Mean Based on
Pooled StDev
---------+---------+---------+---------+
(----------*---------)
(----------*----------)
(--------*---------)
---------+---------+---------+---------+
70
80
90
100
Pooled StDev = 13.78
Data Display
Row
1
2
3
4
5
6
7
8
9
A
96
82
88
70
90
91
87
88
B
65
74
72
66
79
82
73
Data Display
Row
1
2
3
4
C101
692.0
8.0
86.5
60278.0
C
60
73
85
61
79
85
88
79
23
C102
511
7
73
37535
C103
633.0
9.0
70.3
47855.0
MTB > vartest c7 c8
Test for Equal Variances: C7 versus C8
95%
C8
A
B
C
Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
8
4.7074
7.7460 18.9708
7
3.6650
6.2183 16.8724
9 12.7262 20.4145 46.2301
Bartlett's Test (normal distribution)
Test statistic = 10.63, p-value = 0.005
Levene's Test (any continuous distribution)
Test statistic = 1.61, p-value = 0.223
43
252y0541s 5/7/05
Test for Equal Variances: C7 versus C8
Test for Equal Variances for C7
Bartlett's Test
Test Statistic
P-Value
A
10.63
0.005
Lev ene's Test
C8
Test Statistic
P-Value
1.61
0.223
B
C
0
10
20
30
40
95% Bonferroni Confidence Intervals for StDevs
50
MTB > normtest 'A';
SUBC> KSTest.
Probability Plot of A
Probability Plot of A
Normal
99
Mean
StDev
N
KS
P-Value
95
90
86.5
7.746
8
0.276
0.073
Percent
80
70
60
50
40
30
20
10
5
1
70
75
80
85
90
95
100
105
A
44