4/28/00 252cp400s
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Last Computer Problem
The data is below. You need to set up Columns for REV(revenue of the Coca-Cola company 1986 -1996),YEAR(year
with 1986 as zero), YEARSQ (YEAR squared), GDP(Real GDP) and RMINW(Real Minimum Wage) as well as resid
and pred.
Row
REV
YEAR
GDP
RMINW
1
7.0
0
5.5
3.06
2
7.7
1
5.6
2.95
3
8.3
2
5.9
2.83
4
9.0
3
6.1
2.70
5
10.2
4
6.1
2.91
6
11.6
5
6.1
3.12
7
13.0
6
6.2
3.03
8
14.0
7
6.4
2.94
9
16.2
8
6.6
2.87
10
18.0
9
6.7
2.79
11
18.5
10
6.9
2.94
To set up YEARSQ use
LET 'YEARSQ' = 'YEAR'*'YEAR'
To do the problem with all independent variables, you need to do:
Brief K = 3
Regress 'REV' on 4 'YEAR’ ’YEARSQ’ ’GDP’ ’RMINW’ ‘resid’ ’pred’
Plot ‘REV’ * ‘pred’
Explanation:
The 4 in here tells it that there are 4 explanatory (independent) variables. This number must be correct - for example if
it were 3, ‘RMINW’ would be zapped.
Brief K=3 needs to be set only once.
The plot shows how well you did - a perfect prediction gives a 45 degree line.
Check the significance tests on the coefficients of your independent variables. Which are not significant? Which have
the wrong sign? Can you suggest why?
The rest of the assignment:
First: Try replacing the Regress in the instruction above with Stepwise Regression as is done on page 844 of the text.
Second: Do more regressions using Regress and Plot with appropriate changes to the number in the Regress
instruction. First regress ‘REV’ against YEAR alone, then against YEAR and YEARSQ, then YEAR, YEARSQ and
GDP. then try REV against GDP alone. Create a new variable equal to GDP squared. Do GDP and GDP squared do as
well as YEAR and YEARSQ in predicting REV? What about GDP, GDP squared and YEAR? Try the stepwise
regression command with GDP squared added to your independent variables.
1
Worksheet size: 100000 cells
MTB > RETR 'C:\MINITAB\CP4-00.MTW'.
Retrieving worksheet from file: C:\MINITAB\CP4-00.MTW
Worksheet was saved on 4/26/2000
MTB > brief k=3
MTB > regress 'rev' on 4 'year''yearsq''gdp''rminw''resid''pred'
Regression Analysis
The regression equation is
rev = 42.6 + 1.24 year + 0.0618 yearsq - 4.94 gdp - 2.79 rminw
Predictor
Constant
year
yearsq
gdp
rminw
Coef
42.56
1.2360
0.06181
-4.944
-2.792
s = 0.3231
Stdev
14.98
0.2648
0.01117
2.028
1.455
R-sq = 99.6%
t-ratio
2.84
4.67
5.53
-2.44
-1.92
p
0.029
0.003
0.001
0.051
0.103
R-sq(adj) = 99.4%
Analysis of Variance
SOURCE
Regression
Error
Total
DF
4
6
10
SS
169.639
0.626
170.265
SOURCE
year
yearsq
gdp
rminw
DF
1
1
1
1
SEQ SS
166.173
2.844
0.238
0.384
Obs.
1
2
3
4
5
6
7
8
9
10
11
year
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
rev
7.0000
7.7000
8.3000
9.0000
10.2000
11.6000
13.0000
14.0000
16.2000
18.0000
18.5000
MS
42.410
0.104
Fit
6.8231
7.9336
8.2067
9.1259
10.2084
11.4144
13.0872
14.3892
15.7590
17.7748
18.7776
F
406.29
Stdev.Fit
0.2637
0.2276
0.1767
0.2466
0.1608
0.2345
0.1963
0.1464
0.1384
0.2524
0.2912
p
0.000
Residual
0.1769
-0.2336
0.0933
-0.1259
-0.0084
0.1856
-0.0872
-0.3892
0.4410
0.2252
-0.2776
St.Resid
0.95
-1.02
0.34
-0.60
-0.03
0.84
-0.34
-1.35
1.51
1.12
-1.99
MTB > plot 'rev' * 'pred'
2
MTB > stepwise 'rev''year''yearsq''gdp''rminw'
Stepwise Regression
F-to-Enter:
4.00
Response is
Step
Constant
year
T-Ratio
rev
1
5.991
1.229
19.12
on
F-to-Remove:
4.00
4 predictors, with N =
11
2
6.855
0.653
4.67
yearsq
T-Ratio
0.058
4.27
S
0.674
0.395
R-Sq
97.60
99.27
More? (Yes, No, Subcommand, or Help)
SUBC> y
No variables entered or removed
More? (Yes, No, Subcommand, or Help)
SUBC> n
MTB > regress 'rev' on 1 'year''resid''pred'
Regression Analysis
The regression equation is
rev = 5.99 + 1.23 year
Predictor
Constant
year
Coef
5.9909
1.22909
s = 0.6743
Stdev
0.3804
0.06429
R-sq = 97.6%
t-ratio
15.75
19.12
p
0.000
0.000
R-sq(adj) = 97.3%
Analysis of Variance
SOURCE
Regression
Error
Total
Obs.
1
2
3
4
5
6
7
8
9
10
11
DF
1
9
10
year
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
SS
166.17
4.09
170.27
rev
7.000
7.700
8.300
9.000
10.200
11.600
13.000
14.000
16.200
18.000
18.500
MS
166.17
0.45
Fit
5.991
7.220
8.449
9.678
10.907
12.136
13.365
14.595
15.824
17.053
18.282
F
365.45
Stdev.Fit
0.380
0.328
0.280
0.241
0.213
0.203
0.213
0.241
0.280
0.328
0.380
p
0.000
Residual
1.009
0.480
-0.149
-0.678
-0.707
-0.536
-0.365
-0.595
0.376
0.947
0.218
St.Resid
1.81
0.81
-0.24
-1.08
-1.11
-0.83
-0.57
-0.94
0.61
1.61
0.39
3
MTB > regress 'rev' on 2 'year''yearsq''resid''pred'
Regression Analysis
The regression equation is
rev = 6.85 + 0.653 year + 0.0576 yearsq
Predictor
Constant
year
yearsq
Coef
6.8545
0.6533
0.05758
s = 0.3950
Stdev
0.3009
0.1400
0.01348
R-sq = 99.3%
t-ratio
22.78
4.67
4.27
p
0.000
0.000
0.003
R-sq(adj) = 99.1%
Analysis of Variance
SOURCE
Regression
Error
Total
DF
2
8
10
SS
169.017
1.248
170.265
SOURCE
year
yearsq
DF
1
1
SEQ SS
166.173
2.844
Obs.
1
2
3
4
5
6
7
8
9
10
11
year
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
rev
7.000
7.700
8.300
9.000
10.200
11.600
13.000
14.000
16.200
18.000
18.500
MS
84.509
0.156
Fit
6.855
7.565
8.392
9.333
10.389
11.561
12.847
14.249
15.766
17.398
19.145
F
541.67
Stdev.Fit
0.301
0.208
0.165
0.162
0.174
0.180
0.174
0.162
0.165
0.208
0.301
p
0.000
Residual
0.145
0.135
-0.092
-0.333
-0.189
0.039
0.153
-0.249
0.434
0.602
-0.645
St.Resid
0.57
0.40
-0.25
-0.92
-0.53
0.11
0.43
-0.69
1.21
1.79
-2.52R
R denotes an obs. with a large st. resid.
MTB > regress 'rev' on 3 'year''yearsq''gdp''resid''pred'
Regression Analysis
The regression equation is
rev = 16.7 + 0.870 year + 0.0588 yearsq - 1.77 gdp
Predictor
Constant
year
yearsq
gdp
Coef
16.705
0.8698
0.05882
-1.773
s = 0.3800
Stdev
7.684
0.2159
0.01301
1.382
R-sq = 99.4%
t-ratio
2.17
4.03
4.52
-1.28
p
0.066
0.005
0.000
0.240
R-sq(adj) = 99.2%
Analysis of Variance
SOURCE
Regression
Error
Total
DF
3
7
10
SS
169.255
1.011
170.265
SOURCE
year
yearsq
gdp
DF
1
1
1
SEQ SS
166.173
2.844
0.238
MS
56.418
0.144
F
390.81
p
0.000
4
Obs.
1
2
3
4
5
6
7
8
9
10
11
year
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
rev
7.000
7.700
8.300
9.000
10.200
11.600
13.000
14.000
16.200
18.000
18.500
Fit
6.954
7.705
8.219
9.029
10.310
11.709
13.049
14.329
15.726
17.419
19.051
Stdev.Fit
0.300
0.228
0.208
0.284
0.178
0.208
0.230
0.168
0.161
0.201
0.299
Residual
0.046
-0.005
0.081
-0.029
-0.110
-0.109
-0.049
-0.329
0.474
0.581
-0.551
St.Resid
0.20
-0.02
0.25
-0.11
-0.33
-0.34
-0.16
-0.96
1.38
1.80
-2.35R
R denotes an obs. with a large st. resid.
MTB > regress 'rev' on 1 'gdp''resid''pred'
Regression Analysis
The regression equation is
rev = - 44.1 + 9.09 gdp
Predictor
Constant
gdp
Coef
-44.139
9.0900
s = 1.179
Stdev
5.297
0.8537
R-sq = 92.6%
t-ratio
-8.33
10.65
p
0.000
0.000
R-sq(adj) = 91.8%
Analysis of Variance
SOURCE
Regression
Error
Total
Obs.
1
2
3
4
5
6
7
8
9
10
11
DF
1
9
10
gdp
5.50
5.60
5.90
6.10
6.10
6.10
6.20
6.40
6.60
6.70
6.90
SS
157.74
12.52
170.27
rev
7.000
7.700
8.300
9.000
10.200
11.600
13.000
14.000
16.200
18.000
18.500
MS
157.74
1.39
Fit
5.856
6.765
9.492
11.310
11.310
11.310
12.219
14.037
15.855
16.764
18.582
F
113.39
Stdev.Fit
0.689
0.617
0.434
0.364
0.364
0.364
0.356
0.398
0.498
0.562
0.702
p
0.000
Residual
1.144
0.935
-1.192
-2.310
-1.110
0.290
0.781
-0.037
0.345
1.236
-0.082
St.Resid
1.19
0.93
-1.09
-2.06R
-0.99
0.26
0.69
-0.03
0.32
1.19
-0.09
R denotes an obs. with a large st. resid.
MTB > regress 'rev' on 2 'gdp''gdpsq''resid''pred'
Regression Analysis
* NOTE *
* NOTE *
gdp is highly correlated with other
gdpsq is highly correlated with other
predictor variables
predictor variables
The regression equation is
rev = 65.7 - 26.5 gdp + 2.88 gdpsq
Predictor
Constant
gdp
gdpsq
s = 1.085
Coef
65.67
-26.54
2.877
Stdev
67.70
21.92
1.769
R-sq = 94.5%
t-ratio
0.97
-1.21
1.63
p
0.360
0.261
0.143
R-sq(adj) = 93.1%
5
Analysis of Variance
SOURCE
Regression
Error
Total
DF
2
8
10
SS
160.855
9.410
170.265
SOURCE
gdp
gdpsq
DF
1
1
SEQ SS
157.745
3.111
Obs.
1
2
3
4
5
6
7
8
9
10
11
gdp
5.50
5.60
5.90
6.10
6.10
6.10
6.20
6.40
6.60
6.70
6.90
rev
7.000
7.700
8.300
9.000
10.200
11.600
13.000
14.000
16.200
18.000
18.500
MS
80.428
1.176
Fit
6.733
7.273
9.237
10.835
10.835
10.835
11.720
13.662
15.835
17.008
19.526
F
68.38
Stdev.Fit
0.832
0.648
0.428
0.444
0.444
0.444
0.449
0.432
0.458
0.538
0.868
p
0.000
Residual
0.267
0.427
-0.937
-1.835
-0.635
0.765
1.280
0.338
0.365
0.992
-1.026
St.Resid
0.38
0.49
-0.94
-1.85
-0.64
0.77
1.30
0.34
0.37
1.05
-1.58
MTB > regress 'rev' on 3 'gdp''gdpsq''year''resid''pred'
Regression Analysis
* NOTE *
* NOTE *
gdp is highly correlated with other
gdpsq is highly correlated with other
predictor variables
predictor variables
The regression equation is
rev = 114 - 34.2 gdp + 2.68 gdpsq + 1.36 year
Predictor
Constant
gdp
gdpsq
year
Coef
114.01
-34.202
2.6765
1.3642
s = 0.4269
Stdev
27.61
8.705
0.6971
0.2042
R-sq = 99.3%
t-ratio
4.13
-3.93
3.84
6.68
p
0.004
0.006
0.006
0.000
R-sq(adj) = 98.9%
Analysis of Variance
SOURCE
Regression
Error
Total
DF
3
7
10
SS
168.990
1.276
170.265
SOURCE
gdp
gdpsq
year
DF
1
1
1
SEQ SS
157.745
3.111
8.135
Obs.
1
2
3
4
5
6
7
8
9
10
11
gdp
5.50
5.60
5.90
6.10
6.10
6.10
6.20
6.40
6.60
6.70
6.90
rev
7.000
7.700
8.300
9.000
10.200
11.600
13.000
14.000
16.200
18.000
18.500
MS
56.330
0.182
Fit
6.862
7.777
8.114
9.062
10.426
11.790
13.027
14.295
15.778
17.282
19.086
F
309.13
Stdev.Fit
0.328
0.266
0.238
0.318
0.185
0.226
0.263
0.195
0.181
0.216
0.348
p
0.000
Residual
0.138
-0.077
0.186
-0.062
-0.226
-0.190
-0.027
-0.295
0.422
0.718
-0.586
St.Resid
0.51
-0.23
0.52
-0.22
-0.59
-0.53
-0.08
-0.78
1.09
1.95
-2.37R
R denotes an obs. with a large st. resid.
6
MTB > stepwise 'rev''year''yearsq''gdp''gdpsq''rminw'
Stepwise Regression
F-to-Enter:
Response is
4.00
rev
F-to-Remove:
on
5 predictors, with N =
Step
Constant
1
5.991
2
6.855
year
T-Ratio
1.229
19.12
0.653
4.67
yearsq
T-Ratio
4.00
11
0.058
4.27
S
0.674
0.395
R-Sq
97.60
99.27
More? (Yes, No, Subcommand, or Help)
SUBC> y
No variables entered or removed
More? (Yes, No, Subcommand, or Help)
SUBC> y
No variables entered or removed
More? (Yes, No, Subcommand, or Help)
SUBC> n
MTB > print c1-c8
Data Display
Row
rev
year
yearsq
gdp
rminw
gdpsq
resid
pred
1
2
3
4
5
6
7
8
9
10
11
7.0
7.7
8.3
9.0
10.2
11.6
13.0
14.0
16.2
18.0
18.5
0
1
2
3
4
5
6
7
8
9
10
0
1
4
9
16
25
36
49
64
81
100
5.5
5.6
5.9
6.1
6.1
6.1
6.2
6.4
6.6
6.7
6.9
3.06
2.95
2.83
2.70
2.91
3.12
3.03
2.94
2.87
2.79
2.94
30.25
31.36
34.81
37.21
37.21
37.21
38.44
40.96
43.56
44.89
47.61
0.50585
-0.22994
0.52356
-0.21764
-0.58829
-0.52584
-0.07928
-0.77751
1.09065
1.94876
-2.37060
6.8618
7.7768
8.1145
9.0620
10.4262
11.7905
13.0266
14.2953
15.7782
17.2820
19.0860
7