252regress078 12/4/07
I. (25+ points) Do all the following. Note that answers without reasons and/or citation of appropriate
statistical tests receive no credit. Most answers require a statistical test, that is, stating or implying a
hypothesis and showing why it is true or false by citing a table value or a p-value. If you haven’t done it
lately, take a fast look at ECO 252 - Things That You Should Never Do on a Statistics Exam (or Anywhere
Else)
In the Lees’ 2000 text they noted that before 1979 the Federal Reserve targeted
interest rates, letting the money supply grow in such a way that the interest
rates would remain stable. After 1979, the Fed switched to targeting the money
supply. The Lees did a regression of Money supply against GNP (I had to replace
this with GDP.), the prime rate(PrRt) and a dummy variable (Dummy)that is 1
before 1979 and zero from 1979 till 1990, when their analysis stops, They
report a high R-squared, and extremely significant coefficients for the Prime
Rate, GNP and the dummy variable, which seems to tell us that the Fed’s change
of regime had a real effect on the money supply. Later in the text they suggest
the addition of an interaction variable (GDPPR), which is the product of the
Prime rate and the GDP, and a second interaction variable (GDPPR). I added the
year and its square measured from 1958, population, and GDP squared. My attempt
to update the Lees results was terrible discouraging. The dependent variable is
M1 or its logarithm (logM1).
————— 12/3/2007 11:31:46 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\RBOVE\My
Documents\Minitab\M1PrRGDP.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\M1PrRGDP.MTW'
Worksheet was saved on Mon Dec 03 2007
MTB > print c5 c2 c4 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15
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
C5
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
M1
140.0
140.7
145.2
147.8
153.3
160.3
167.8
172.0
183.3
197.4
203.9
214.4
228.3
249.2
262.9
274.2
287.1
306.2
330.9
357.3
381.8
408.5
436.7
474.8
521.4
551.6
619.8
724.7
750.2
786.7
792.9
824.7
896.9
1024.8
1129.7
1150.7
1127.4
PrRt
4.50
5.00
4.50
4.50
4.50
4.50
4.50
5.52
5.50
6.50
8.23
8.00
5.50
5.04
7.49
11.54
7.07
7.20
6.75
8.63
11.65
12.63
20.03
16.50
10.50
12.60
9.78
8.50
8.25
9.00
11.07
10.00
8.50
6.50
6.00
7.25
9.00
GDP
$506.60
$526.40
$544.70
$585.60
$617.70
$663.60
$719.10
$787.80
$832.60
$910.00
$984.60
$1,038.50
$1,127.10
$1,238.30
$1,382.70
$1,500.00
$1,638.30
$1,825.30
$2,030.90
$2,294.70
$2,563.30
$2,789.50
$3,128.40
$3,255.00
$3,536.70
$3,933.20
$4,220.30
$4,462.80
$4,739.50
$5,103.80
$5,484.40
$5,803.10
$5,995.90
$6,337.70
$6,657.40
$7,072.20
$7,397.70
Dummy
1
1
1
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
0
0
0
0
GDPPr
2280
2632
2451
2635
2780
2986
3236
4349
4579
5915
8103
8308
6199
6241
10356
17310
11583
13142
13709
19803
29862
35231
62662
53708
37135
49558
41275
37934
39101
45934
60712
58031
50965
41195
39944
51273
66579
GDPdum
506.6
526.4
544.7
585.6
617.7
663.6
719.1
787.8
832.6
910.0
984.6
1038.5
1127.1
1238.3
1382.7
1500.0
1638.3
1825.3
2030.9
2294.7
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
year
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
yearsq
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729
784
841
900
961
1024
1089
1156
1225
1296
1369
252regress078 12/4/07
38
39
40
41
42
43
44
45
46
47
48
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
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
1081.4
1072.8
1095.9
1123.0
1087.7
1182.0
1219.5
1305.5
1375.2
1373.2
1365.9
Pop
176289
179979
182992
185771
188483
191141
193526
195576
197457
199399
201385
203984
206827
209284
211357
213342
215465
217583
219760
222095
224567
227225
229466
231664
233792
235825
237924
240133
242289
244499
246819
249623
252981
256514
259919
263126
266278
269394
272647
275854
279040
282217
285226
288126
290796
293638
296507
299398
8.25
8.50
8.50
7.75
9.50
6.98
4.75
4.22
4.01
6.01
8.02
GDPsq
256644
277097
296698
342927
381553
440365
517105
620629
693223
828100
969437
1078482
1270354
1533387
1911859
2250000
2684027
3331720
4124555
5265648
6570507
7781310
9786887
10595025
12508247
15470062
17810932
19916584
22462860
26048774
30078643
33675970
35950817
40166441
44320975
50016013
54725965
61103926
68961398
76510009
85903239
96373489
102576384
109612524
120139137
136560259
154601869
174100108
$7,816.90
$8,304.30
$8,747.00
$9,268.40
$9,817.00
$10,128.00
$10,469.60
$10,960.80
$11,685.90
$12,433.90
$13,194.70
log M1
4.94164
4.94663
4.97811
4.99586
5.03240
5.07705
5.12277
5.14749
5.21112
5.28523
5.31763
5.36784
5.43066
5.51826
5.57177
5.61386
5.65983
5.72424
5.80182
5.87858
5.94490
6.01249
6.07925
6.16289
6.25652
6.31282
6.42940
6.58576
6.62034
6.66785
6.67570
6.71502
6.79894
6.93225
7.02971
7.04813
7.02767
6.98601
6.97803
6.99933
7.02376
6.99182
7.07496
7.10620
7.17434
7.22635
7.22490
7.21957
logM1l
4.89222
4.94164
4.94663
4.97811
4.99586
5.03240
5.07705
5.12277
5.14749
5.21112
5.28523
5.31763
5.36784
5.43066
5.51826
5.57177
5.61386
5.65983
5.72424
5.80182
5.87858
5.94490
6.01249
6.07925
6.16289
6.25652
6.31282
6.42940
6.58576
6.62034
6.66785
6.67570
6.71502
6.79894
6.93225
7.02971
7.04813
7.02767
6.98601
6.97803
6.99933
7.02376
6.99182
7.07496
7.10620
7.17434
7.22635
7.22490
0
0
0
0
0
0
0
0
0
0
0
64489
70587
74350
71830
93262
70693
49731
46255
46860
74728
105821
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
38
39
40
41
42
43
44
45
46
47
48
1444
1521
1600
1681
1764
1849
1936
2025
2116
2209
2304
252regress078 12/4/07
I followed the course suggested by the textbook to find what variables were actually important in predicting
the money supply.
Results for: M1PrRGDP.MTW
MTB > Regress c2 5 c4 c6 c7 c10 c12;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
Brief 2.
Regression 1
Regression Analysis: M1 versus PrRt, GDP, Dummy, year, Pop
The regression equation is
M1 = 2874 - 19.1 PrRt + 0.0714 GDP - 115 Dummy + 46.2 year - 0.0149 Pop
Predictor
Coef
SE Coef
T
Constant
2874
1232
2.33
PrRt
-19.116
3.941 -4.85
GDP
0.07138
0.01762
4.05
Dummy
-114.81
48.62 -2.36
year
46.23
15.57
2.97
Pop
-0.014888 0.007176 -2.07
S = 57.7863
R-Sq = 98.4%
R-Sq(adj)
Analysis of Variance
Source
DF
SS
Regression
5 8498077
Residual Error 42
140249
Total
47 8638326
Source
PrRt
GDP
Dummy
year
Pop
DF
1
1
1
1
1
MS
1699615
3339
P
VIF
0.025
0.000
2.241
0.000
62.461
0.023
8.260
0.005 668.523
0.044 917.418
= 98.2%
F
508.98
P
0.000
Seq SS
3746
8260319
139454
80187
14371
Unusual Observations
Obs PrRt
M1
Fit SE Fit Residual St Resid
23 20.0
436.70 361.08
37.33
75.62
1.71 X
35
6.0 1129.70 982.60
18.35
147.10
2.68R
36
7.3 1150.70 986.80
14.01
163.90
2.92R
37
9.0 1127.40 975.89
11.81
151.51
2.68R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
So the regression above was my first attempt. There are several questions that can be asked at this point.
1) Why does this regression look awfully good as far as significance and the amount of the variation in the
Y variable that is explained by the equation? (3)
2) There are only two coefficients here whose sign you can predict in advance. What are they, what did you
predict and why and were you right? (2)
3) What does the Analysis of Variance tell us? What hypothesis did it cause you to reject?(1)
252regress078 12/4/07
MTB > Regress c2 4 c4 c6 c7 c10 ;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
Brief 2.
Regression 2
Regression Analysis: M1 versus PrRt, GDP, Dummy, year
The regression equation is
M1 = 321 - 20.7 PrRt + 0.0415 GDP - 174 Dummy + 14.5 year
Predictor
Coef SE Coef
Constant
321.24
66.06
PrRt
-20.668
4.016
GDP
0.04152 0.01055
Dummy
-173.71
40.96
year
14.530
3.077
S = 59.9651
R-Sq = 98.2%
T
P
VIF
4.86 0.000
-5.15 0.000
2.160
3.94 0.000 20.791
-4.24 0.000
5.444
4.72 0.000 24.254
R-Sq(adj) = 98.0%
Analysis of Variance
Source
DF
SS
Regression
4 8483706
Residual Error 43
154620
Total
47 8638326
MS
2120927
3596
Source
PrRt
GDP
Dummy
year
DF
1
1
1
1
F
589.83
P
0.000
Seq SS
3746
8260319
139454
80187
Unusual Observations
Obs PrRt
M1
Fit SE Fit Residual St Resid
23 20.0
436.70 371.34
38.39
65.36
1.42 X
35
6.0 1129.70 982.21
19.04
147.49
2.59R
36
7.3 1150.70 988.13
14.53
162.57
2.79R
37
9.0 1127.40 980.00
12.08
147.40
2.51R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
MTB > Regress c2 3 c4 c6 c7 ;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
Brief 2.
Regression 3
Regression Analysis: M1 versus PrRt, GDP, Dummy
The regression equation is
M1 = 451 - 14.3 PrRt + 0.0865 GDP - 240 Dummy
Predictor
Coef
SE Coef
T
P
VIF
Constant
450.99
73.19
6.16 0.000
PrRt
-14.269
4.605 -3.10 0.003 1.914
GDP
0.086456 0.005548 15.58 0.000 3.875
Dummy
-239.76
46.90 -5.11 0.000 4.809
S = 73.0515
R-Sq = 97.3%
R-Sq(adj) = 97.1%
Analysis of Variance
Source
DF
SS
Regression
3 8403519
Residual Error 44
234807
Total
47 8638326
Source
PrRt
GDP
Dummy
DF
1
1
1
Seq SS
3746
8260319
139454
MS
2801173
5337
F
524.91
P
0.000
252regress078 12/4/07
Unusual Observations
Obs PrRt
M1
Fit SE Fit Residual St Resid
23 20.0
436.7 435.7
43.7
1.0
0.02 X
35
6.0 1129.7 941.0
20.6
188.7
2.69R
36
7.3 1150.7 959.0
16.0
191.7
2.69R
37
9.0 1127.4 962.1
14.0
165.3
2.30R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
4) What did I do to get from Regression 1 to regression 3 and why? (2)
5) Why was I now ready to quit dropping variables and do a ‘best subsets’ regression? (1) [9]
6) What would the money supply be that would be predicted for 1970 assuming that the numbers given for
1970 are correct? By what percent is it off the actual value? (2)
7) Can you make this into a rough prediction interval? Does this include the actual value for 1970? (2) [13]
MTB > BReg c2 c4 c6 c7 ;
SUBC>
NVars 1 3;
SUBC>
Best 2;
SUBC>
Constant.
Regression 4
Best Subsets Regression: M1 versus PrRt, GDP, Dummy
Response is M1
Vars
1
1
2
2
3
R-Sq
95.6
67.8
96.7
95.7
97.3
R-Sq(adj)
95.6
67.1
96.5
95.5
97.1
Mallows
Cp
26.5
477.7
11.6
28.1
4.0
S
90.432
246.02
79.727
91.197
73.051
D
P
u
r G m
R D m
t P y
X
X
X X
X X
X X X
8) What is Regression 4 telling me to do? Why can you say that? (2)
252regress078 12/4/07
MTB > Regress c2 3 c4 c6 c7 ;
SUBC>
GFourpack;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
Regression 5
Regression Analysis: M1 versus PrRt, GDP, Dummy
The regression equation is
M1 = 451 - 14.3 PrRt + 0.0865 GDP - 240 Dummy
Predictor
Coef
SE Coef
T
P
VIF
Constant
450.99
73.19
6.16 0.000
PrRt
-14.269
4.605 -3.10 0.003 1.914
GDP
0.086456 0.005548 15.58 0.000 3.875
Dummy
-239.76
46.90 -5.11 0.000 4.809
S = 73.0515
R-Sq = 97.3%
R-Sq(adj) = 97.1%
Analysis of Variance
Source
DF
SS
Regression
3 8403519
Residual Error 44
234807
Total
47 8638326
Source
PrRt
GDP
Dummy
DF
1
1
1
MS
2801173
5337
F
524.91
P
0.000
Seq SS
3746
8260319
139454
Unusual Observations
Obs PrRt
M1
Fit SE Fit Residual St Resid
23 20.0
436.7 435.7
43.7
1.0
0.02 X
35
6.0 1129.7 941.0
20.6
188.7
2.69R
36
7.3 1150.7 959.0
16.0
191.7
2.69R
37
9.0 1127.4 962.1
14.0
165.3
2.30R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Durbin-Watson statistic = 0.445619
Residual Plots for M1
252regress078 12/4/07
9) Regression 5 is just a repeat of regression 3, but now I am doing residual analysis. What are the DurbinWatson statistic and the plot of residuals vs. order telling me is present? What 2 conditions for regression
seem to be being violated? (3) [18]
MTB > Regress c2 4 c4 c6 c7 c13;
SUBC>
GFourpack;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
Regression 6
Regression Analysis: M1 versus PrRt, GDP, Dummy, GDPsq
The regression equation is
M1 = 131 - 13.1 PrRt + 0.187 GDP - 26.3 Dummy - 0.000007 GDPsq
Predictor
Coef
SE Coef
T
P
Constant
131.36
64.18
2.05 0.047
PrRt
-13.142
3.050 -4.31 0.000
GDP
0.18659
0.01370 13.62 0.000
Dummy
-26.33
41.88 -0.63 0.533
GDPsq
-0.00000671 0.00000088 -7.59 0.000
S = 48.3231
R-Sq = 98.8%
R-Sq(adj) = 98.7%
Analysis of Variance
Source
DF
SS
Regression
4 8537916
Residual Error 43
100410
Total
47 8638326
Source
PrRt
GDP
Dummy
GDPsq
DF
1
1
1
1
MS
2134479
2335
F
914.07
VIF
1.919
53.994
8.764
33.120
P
0.000
Seq SS
3746
8260319
139454
134396
Unusual Observations
Obs PrRt
M1
Fit SE Fit Residual St Resid
23 20.0
436.70
386.21
29.65
50.49
1.32 X
35
6.0 1129.70
997.46
15.53
132.24
2.89R
36
7.3 1150.70 1020.24
13.32
130.46
2.81R
37
9.0 1127.40 1026.39
12.53
101.01
2.16R
42
9.5 1087.70 1191.94
14.93
-104.24
-2.27R
48
8.0 1365.90 1320.38
30.91
45.52
1.23 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Durbin-Watson statistic = 0.551845
252regress078 12/4/07
Residual Plots for M1
10) I now felt free to add the square of GDP as a new independent variable? What happened to the VIFs?
Do I care? Why? (2)
11) What did adding the square of GDP do to the significance of my coefficients and the fraction of the
variation of Y that is explained by the equation? (2) [22]
MTB > let c14 = loge (c2)
MTB > Regress c14 4 c4 c6 c7 c13;
SUBC>
GFourpack;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
Regression 7
Regression Analysis: log M1 versus PrRt, GDP, Dummy, GDPsq
The regression equation is
log M1 = 4.79 + 0.00846 PrRt + 0.000453 GDP + 0.0289 Dummy - 0.000000 GDPsq
Predictor
Coef
SE Coef
T
P
Constant
4.7882
0.1358
35.26 0.000
PrRt
0.008461
0.006453
1.31 0.197
GDP
0.00045309 0.00002899
15.63 0.000
Dummy
0.02889
0.08862
0.33 0.746
GDPsq
-0.00000002 0.00000000 -11.66 0.000
S = 0.102246
R-Sq = 98.5%
R-Sq(adj) = 98.4%
Analysis of Variance
Source
DF
SS
Regression
4 29.3981
Residual Error 43
0.4495
Total
47 29.8476
MS
7.3495
0.0105
F
703.01
P
0.000
VIF
1.919
53.994
8.764
33.120
252regress078 12/4/07
Source
PrRt
GDP
Dummy
GDPsq
DF
1
1
1
1
Seq SS
1.2680
25.6375
1.0725
1.4202
Unusual Observations
Obs PrRt log M1
Fit SE Fit Residual St Resid
23 20.0 6.0792 6.1618 0.0627
-0.0826
-1.02 X
42
9.5 6.9918 7.2158 0.0316
-0.2239
-2.30R
48
8.0 7.2196 7.0393 0.0654
0.1803
2.29RX
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Durbin-Watson statistic = 0.306367
Residual Plots for log M1
12) I just replaced the money supply by its logarithm. The residual analysis tells me this was a sort of good
idea? What does that mean? (1)[23]
13) What is really weird about these coefficients? Which one has the wrong sign? (1)
252regress078 12/4/07
MTB > Regress c14 3 c4 c6
SUBC>
GFourpack;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
c13;
Regression 8
Regression Analysis: log M1 versus PrRt, GDP, GDPsq
The regression equation is
log M1 = 4.83 + 0.00732 PrRt + 0.000445 GDP - 0.000000 GDPsq
Predictor
Coef
SE Coef
T
P
Constant
4.83016
0.04310 112.06 0.000
PrRt
0.007316
0.005359
1.37 0.179
GDP
0.00044536 0.00001650
26.99 0.000
GDPsq
-0.00000002 0.00000000 -15.60 0.000
S = 0.101203
R-Sq = 98.5%
R-Sq(adj) = 98.4%
Analysis of Variance
Source
DF
SS
Regression
3 29.3970
Residual Error 44
0.4506
Total
47 29.8476
Source
PrRt
GDP
GDPsq
DF
1
1
1
MS
9.7990
0.0102
F
956.75
VIF
1.351
17.854
18.176
P
0.000
Seq SS
1.2680
25.6375
2.4915
Unusual Observations
Obs
23
42
48
PrRt
20.0
9.5
8.0
log M1
6.0792
6.9918
7.2196
Fit
6.1606
7.2104
7.0413
SE Fit
0.0620
0.0267
0.0644
Residual
-0.0814
-0.2186
0.1783
St Resid
-1.02 X
-2.24R
2.28RX
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Durbin-Watson statistic = 0.289829
Residual Plots for log M1
252regress078 12/4/07
MTB > Regress c14 2
SUBC>
GFourpack;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
c6
c13;
Regression 9
Regression Analysis: log M1 versus GDP, GDPsq
The regression equation is
log M1 = 4.87 + 0.000457 GDP - 0.000000 GDPsq
Predictor
Coef
SE Coef
T
P
Constant
4.87027
0.03184 152.96 0.000
GDP
0.00045654 0.00001446
31.58 0.000
GDPsq
-0.00000002 0.00000000 -18.76 0.000
S = 0.102169
R-Sq = 98.4%
R-Sq(adj) = 98.4%
Analysis of Variance
Source
DF
SS
Regression
2 29.378
Residual Error 45
0.470
Total
47 29.848
Source
GDP
GDPsq
DF
1
1
MS
14.689
0.010
F
1407.18
VIF
13.455
13.455
P
0.000
Seq SS
25.705
3.673
Unusual Observations
Obs
GDP log M1
Fit SE Fit Residual St Resid
42
9817 6.9918 7.1988 0.0256
-0.2070
-2.09R
47 12434 7.2249 7.0925 0.0478
0.1324
1.47 X
48 13195 7.2196 7.0041 0.0590
0.2154
2.58RX
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Durbin-Watson statistic = 0.208342
Residual Plots for log M1
252regress078 12/4/07
MTB > Regress c14 3
SUBC>
GFourpack;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
c6
c13 c8;
Regression 10
Regression Analysis: log M1 versus GDP, GDPsq, GDPPr
The regression equation is
log M1 = 4.87 + 0.000465 GDP - 0.000000 GDPsq - 0.000001 GDPPr
Predictor
Coef
SE Coef
T
P
VIF
Constant
4.86787
0.03240 150.23 0.000
GDP
0.00046548 0.00002208
21.08 0.000 30.892
GDPsq
-0.00000002 0.00000000 -16.38 0.000 17.958
GDPPr
-0.00000070 0.00000130
-0.54 0.593
5.889
S = 0.102985
R-Sq = 98.4%
R-Sq(adj) = 98.3%
Analysis of Variance
Source
DF
SS
Regression
3 29.3810
Residual Error 44
0.4667
Total
47 29.8476
MS
9.7937
0.0106
F
923.42
P
0.000
Source DF
Seq SS
GDP
1 25.7052
GDPsq
1
3.6727
GDPPr
1
0.0031
Unusual Observations
Obs
GDP log M1
Fit SE Fit Residual St Resid
42
9817 6.9918 7.1826 0.0396
-0.1908
-2.01R
48 13195 7.2196 6.9803 0.0741
0.2393
3.35RX
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Durbin-Watson statistic = 0.196041
14) What has happened to significance and the fraction of the variation in the dependent variable explained
by the regression in Regressions 8), 9) and 10.? In terms of significance etc. which of these 3 is the ‘best’
regression? Why would the Chairman of the FRB be very annoyed? (3) [27]
Residual Plots for log M1
MTB > Regress c14 4
SUBC>
GFourpack;
SUBC>
RType 1;
SUBC>
Constant;
SUBC>
VIF;
SUBC>
DW;
SUBC>
Brief 2.
c6
Not Shown.
c13 c8
c15;
Regression 11
Regression Analysis: log M1 versus GDP, GDPsq, GDPPr, logM1l
The regression equation is
log M1 = - 0.174 + 0.000001 GDP - 0.000000 GDPsq - 0.000001 GDPPr + 1.04 logM1l
Predictor
Coef
SE Coef
T
Constant
-0.1738
0.2820 -0.62
GDP
0.00000085 0.00002708
0.03
GDPsq
-0.00000000 0.00000000 -0.36
GDPPr
-0.00000109 0.00000045 -2.39
logM1l
1.04474
0.05838 17.89
S = 0.0358443
R-Sq = 99.8%
R-Sq(adj) =
P
0.541
0.975
0.723
0.021
0.000
99.8%
VIF
383.407
136.981
5.902
80.236
252regress078 12/4/07
Analysis of Variance
Source
DF
SS
Regression
4 29.7924
Residual Error 43
0.0552
Total
47 29.8476
Source
GDP
GDPsq
GDPPr
logM1l
DF
1
1
1
1
MS
7.4481
0.0013
F
5797.02
P
0.000
Seq SS
25.7052
3.6727
0.0031
0.4114
Unusual Observations
Obs
28
37
38
48
GDP
4463
7398
7817
13195
log M1
6.58576
7.02767
6.98601
7.21957
Fit
6.49641
7.09767
7.07589
7.18793
SE Fit
0.00824
0.00984
0.00849
0.02830
Residual
0.08935
-0.07000
-0.08988
0.03164
St Resid
2.56R
-2.03R
-2.58R
1.44 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Durbin-Watson statistic = 1.17315
Residual Plots for log M1
Not displayed.
15) So what problem did this fix? Incidentally what I added to the independent variables was the money
supply of the previous period? (1) [28]