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 C5 M1 PrRt GDP Dummy GDPPr GDPdum year yearsq

1 1959 140.0 4.50 $506.60 1 2280 506.6 1 1

2 1960 140.7 5.00 $526.40 1 2632 526.4 2 4

3 1961 145.2 4.50 $544.70 1 2451 544.7 3 9

4 1962 147.8 4.50 $585.60 1 2635 585.6 4 16

5 1963 153.3 4.50 $617.70 1 2780 617.7 5 25

6 1964 160.3 4.50 $663.60 1 2986 663.6 6 36

7 1965 167.8 4.50 $719.10 1 3236 719.1 7 49

8 1966 172.0 5.52 $787.80 1 4349 787.8 8 64

9 1967 183.3 5.50 $832.60 1 4579 832.6 9 81

10 1968 197.4 6.50 $910.00 1 5915 910.0 10 100

11 1969 203.9 8.23 $984.60 1 8103 984.6 11 121

12 1970 214.4 8.00 $1,038.50 1 8308 1038.5 12 144

13 1971 228.3 5.50 $1,127.10 1 6199 1127.1 13 169

14 1972 249.2 5.04 $1,238.30 1 6241 1238.3 14 196

15 1973 262.9 7.49 $1,382.70 1 10356 1382.7 15 225

16 1974 274.2 11.54 $1,500.00 1 17310 1500.0 16 256

17 1975 287.1 7.07 $1,638.30 1 11583 1638.3 17 289

18 1976 306.2 7.20 $1,825.30 1 13142 1825.3 18 324

19 1977 330.9 6.75 $2,030.90 1 13709 2030.9 19 361

20 1978 357.3 8.63 $2,294.70 1 19803 2294.7 20 400

21 1979 381.8 11.65 $2,563.30 0 29862 0.0 21 441

22 1980 408.5 12.63 $2,789.50 0 35231 0.0 22 484

23 1981 436.7 20.03 $3,128.40 0 62662 0.0 23 529

24 1982 474.8 16.50 $3,255.00 0 53708 0.0 24 576

25 1983 521.4 10.50 $3,536.70 0 37135 0.0 25 625

26 1984 551.6 12.60 $3,933.20 0 49558 0.0 26 676

27 1985 619.8 9.78 $4,220.30 0 41275 0.0 27 729

28 1986 724.7 8.50 $4,462.80 0 37934 0.0 28 784

29 1987 750.2 8.25 $4,739.50 0 39101 0.0 29 841

30 1988 786.7 9.00 $5,103.80 0 45934 0.0 30 900

31 1989 792.9 11.07 $5,484.40 0 60712 0.0 31 961

32 1990 824.7 10.00 $5,803.10 0 58031 0.0 32 1024

33 1991 896.9 8.50 $5,995.90 0 50965 0.0 33 1089

34 1992 1024.8 6.50 $6,337.70 0 41195 0.0 34 1156

35 1993 1129.7 6.00 $6,657.40 0 39944 0.0 35 1225

36 1994 1150.7 7.25 $7,072.20 0 51273 0.0 36 1296

37 1995 1127.4 9.00 $7,397.70 0 66579 0.0 37 1369

38 1996 1081.4 8.25 $7,816.90 0 64489 0.0 38 1444

39 1997 1072.8 8.50 $8,304.30 0 70587 0.0 39 1521

40 1998 1095.9 8.50 $8,747.00 0 74350 0.0 40 1600

41 1999 1123.0 7.75 $9,268.40 0 71830 0.0 41 1681

42 2000 1087.7 9.50 $9,817.00 0 93262 0.0 42 1764

43 2001 1182.0 6.98 $10,128.00 0 70693 0.0 43 1849

44 2002 1219.5 4.75 $10,469.60 0 49731 0.0 44 1936

45 2003 1305.5 4.22 $10,960.80 0 46255 0.0 45 2025

46 2004 1375.2 4.01 $11,685.90 0 46860 0.0 46 2116

47 2005 1373.2 6.01 $12,433.90 0 74728 0.0 47 2209

48 2006 1365.9 8.02 $13,194.70 0 105821 0.0 48 2304

Row Pop GDPsq log M1 logM1l

1 176289 256644 4.94164 4.89222

2 179979 277097 4.94663 4.94164

3 182992 296698 4.97811 4.94663

4 185771 342927 4.99586 4.97811

5 188483 381553 5.03240 4.99586

6 191141 440365 5.07705 5.03240

7 193526 517105 5.12277 5.07705

8 195576 620629 5.14749 5.12277

9 197457 693223 5.21112 5.14749

10 199399 828100 5.28523 5.21112

11 201385 969437 5.31763 5.28523

12 203984 1078482 5.36784 5.31763

13 206827 1270354 5.43066 5.36784

14 209284 1533387 5.51826 5.43066

15 211357 1911859 5.57177 5.51826

16 213342 2250000 5.61386 5.57177

17 215465 2684027 5.65983 5.61386

18 217583 3331720 5.72424 5.65983

19 219760 4124555 5.80182 5.72424

20 222095 5265648 5.87858 5.80182

21 224567 6570507 5.94490 5.87858

22 227225 7781310 6.01249 5.94490

23 229466 9786887 6.07925 6.01249

24 231664 10595025 6.16289 6.07925

25 233792 12508247 6.25652 6.16289

26 235825 15470062 6.31282 6.25652

27 237924 17810932 6.42940 6.31282

28 240133 19916584 6.58576 6.42940

29 242289 22462860 6.62034 6.58576

30 244499 26048774 6.66785 6.62034

31 246819 30078643 6.67570 6.66785

32 249623 33675970 6.71502 6.67570

33 252981 35950817 6.79894 6.71502

34 256514 40166441 6.93225 6.79894

35 259919 44320975 7.02971 6.93225

36 263126 50016013 7.04813 7.02971

37 266278 54725965 7.02767 7.04813

38 269394 61103926 6.98601 7.02767

39 272647 68961398 6.97803 6.98601

40 275854 76510009 6.99933 6.97803

41 279040 85903239 7.02376 6.99933

42 282217 96373489 6.99182 7.02376

43 285226 102576384 7.07496 6.99182

44 288126 109612524 7.10620 7.07496

45 290796 120139137 7.17434 7.10620

46 293638 136560259 7.22635 7.17434

47 296507 154601869 7.22490 7.22635

48 299398 174100108 7.21957 7.22490

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; Regression 1

SUBC> Constant;

SUBC> VIF;

SUBC> Brief 2.

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 P VIF

Constant 2874 1232 2.33 0.025

PrRt -19.116 3.941 -4.85 0.000 2.241

GDP 0.07138 0.01762 4.05 0.000 62.461

Dummy -114.81 48.62 -2.36 0.023 8.260

year 46.23 15.57 2.97 0.005 668.523

Pop -0.014888 0.007176 -2.07 0.044 917.418

S = 57.7863 R-Sq = 98.4% R-Sq(adj) = 98.2%

Analysis of Variance

Source DF SS MS F P

Regression 5 8498077 1699615 508.98 0.000

Residual Error 42 140249 3339

Total 47 8638326

Source DF Seq SS

PrRt 1 3746

GDP 1 8260319

Dummy 1 139454

year 1 80187

Pop 1 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)

MTB > Regress c2 4 c4 c6 c7 c10 ; Regression 2

SUBC> Constant;

SUBC> VIF;

SUBC> Brief 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 T P VIF

Constant 321.24 66.06 4.86 0.000

PrRt -20.668 4.016 -5.15 0.000 2.160

GDP 0.04152 0.01055 3.94 0.000 20.791

Dummy -173.71 40.96 -4.24 0.000 5.444

year 14.530 3.077 4.72 0.000 24.254

S = 59.9651 R-Sq = 98.2% R-Sq(adj) = 98.0%

Analysis of Variance

Source DF SS MS F P

Regression 4 8483706 2120927 589.83 0.000

Residual Error 43 154620 3596

Total 47 8638326

Source DF Seq SS

PrRt 1 3746

GDP 1 8260319

Dummy 1 139454

year 1 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 ; Regression 3

SUBC> Constant;

SUBC> VIF;

SUBC> Brief 2.

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 MS F P

Regression 3 8403519 2801173 524.91 0.000

Residual Error 44 234807 5337

Total 47 8638326

Source DF Seq SS

PrRt 1 3746

GDP 1 8260319

Dummy 1 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.

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 ; Regression 4

SUBC> NVars 1 3;

SUBC> Best 2;

SUBC> Constant.

Best Subsets Regression: M1 versus PrRt, GDP, Dummy

Response is M1

D

P u

r G m

Mallows R D m

Vars R-Sq R-Sq(adj) Cp S t P y

1 95.6 95.6 26.5 90.432 X

1 67.8 67.1 477.7 246.02 X

2 96.7 96.5 11.6 79.727 X X

2 95.7 95.5 28.1 91.197 X X

3 97.3 97.1 4.0 73.051 X X X

8) What is Regression 4 telling me to do? Why can you say that? (2)

MTB > Regress c2 3 c4 c6 c7 ; Regression 5

SUBC> GFourpack;

SUBC> RType 1;

SUBC> Constant;

SUBC> VIF;

SUBC> DW;

SUBC> Brief 2.

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 MS F P

Regression 3 8403519 2801173 524.91 0.000

Residual Error 44 234807 5337

Total 47 8638326

Source DF Seq SS

PrRt 1 3746

GDP 1 8260319

Dummy 1 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

9) Regression 5 is just a repeat of regression 3, but now I am doing residual analysis. What are the Durbin-Watson 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; Regression 6

SUBC> GFourpack;

SUBC> RType 1;

SUBC> Constant;

SUBC> VIF;