3. Using the data provided, perform the following operations: a) Run the regress

ID: 3205810 • Letter: 3

Question

3. Using the data provided, perform the following operations: a) Run the regression, where ct is real consumption and yt is real GNP (i.e., divide by the price level). Report estimates of a and B. Do not use any statistical package. You may use a spreadsheet program to manipulate numbers. b) Report t-statistics for a and B. c) Report an F-statistic for the regression equation. d) Report an R2 for the regression equation. e) What is a 95% confidence interval for B? f If al GNP is 80, what is your prediction for real consumption? Pro- vide a 90% confidence interval.

Explanation / Answer

Year

GNP

Real GNP

Disposable Income

Net Personal Saving as Percentage of Disposable Income

Personal Saving

Consumption

1929

103.1

203.6

83.3

4.165

79.135

1931

75.8

169.3

4.1

2.624

61.376

1933

55.6

141.5

45.5

-2

-0.91

46.41

1935

72.7

159.5

58.5

3.7

2.1645

56.3355

1937

90.4

203.2

71.2

5.3

3.7736

67.4264

1938

84.7

192.9

65.5

1.1

0.7205

64.7795

1939

90.5

209.4

70.3

3.7

2.6011

67.6989

1940

99.7

227.2

75.7

5.1

3.8607

71.8393

1941

124.5

263.7

92.7

11.8

10.9386

81.7614

1942

157.9

297.8

116.9

23.6

27.5884

89.3116

1944

210.1

361.3

146.3

25.5

37.3065

108.9935

1945

212

355.2

150.2

19.7

29.5894

120.6106

1946

208.5

312.6

160

9.5

15.2

144.8

1948

257.6

323.7

189.1

7.1

13.4261

175.6739

1949

256.5

324.1

188.6

9.43

179.17

1950

284.8

355.3

206.9

6.3

13.0347

193.8653

1951

328.4

383.4

226.6

7.6

17.2216

209.3784

1952

345.5

395.1

238.3

7.6

18.1108

220.1892

1953

364.6

412.8

252.6

7.2

18.1872

234.4128

1954

364.8

407

257.4

6.4

16.4736

240.9264

1955

398

438

275.3

5.7

15.6921

259.6079

1956

419.2

446.1

293.2

20.524

272.676

1957

441.1

452.5

308.5

6.7

20.6695

287.8305

1958

447.3

318.8

22.316

296.484

1959

483.7

475.9

337.3

5.6

18.8888

318.4112

1960

503.8

487.7

350

4.9

17.15

332.85

1961

520.1

497.2

364.4

5.8

21.1352

343.2648

1962

580.3

529.8

385.3

5.6

21.5768

363.7232

1963

590.5

551

404.6

4.9

19.8254

384.7746

Personal Saving=Disposable Income* Net Personal Saving as Percentage of Disposable Income/100

Consumption= Disposable Income- Personal Saving

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.961007

R Square

0.923535

Adjusted R Square

0.920703

Standard Error

30.51784

Observations

ANOVA

Significance F

Regression

303713.7

326.1046

1.33E-16

Residual

25146.14

931.3383

Total

328859.9

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-114.401

17.53712

-6.52334

5.39E-07

-150.384

-78.4174