Exercise econometrics 5.9.

...

a. Estimate the preceding model.

[pic 34]

b. From the estimated residuals, find out if the normality assumption can be sustained.

[pic 35]

Distribución de frecuencias para uhat1, observaciones 1-36

número de cajas = 7, media = -3,15797e-015, desv.típ.=1,58192

intervalo punto medio frecuencia rel acum.

-1,7958 - -0,84121 -1,3185 6 16,67% 33,33% ******

-0,84121 - 0,11340 -0,36391 5 13,89% 47,22% ****

0,11340 - 1,0680 0,59071 11 30,56% 77,78% ***********

1,0680 - 2,0226 1,5453 4 11,11% 88,89% ***

2,0226 - 2,9773 2,5000 2 5,56% 94,44% *

>= 2,9773 3,4546 2 5,56% 100,00% *

Contraste de la hipótesis nula de distribución normal:

Chi-cuadrado(2) = 1,286 con valor p 0,52568

c. Now test the hypothesis that β2 = 1, that is, there is a one-to-one correspondence between male and female math scores.

t(34, .025) = 2,032

Variable

Coeficiente

Intervalo de confianza 95%

const

198,737

(172,571, 224,903)

Female

0,670482

(0,616694, 0,724270)

- Set up the ANOVA table for this problem.

Análisis de Varianza:

Suma de cuadrados gl Media de cuadrados

Regresión 1605,92 1 1605,92

Residuo 85,0838 34 2,50246

Total 1691 35 49,7353

R^2 = 1605,92 / 1691 = 0,949684

F(1, 34) = 1605,92 / 2,50246 = 641,734

5.18. Repeat the exercise in the preceding problem but let Y and X denote the

male and female verbal scores, respectively.

[pic 36]

[pic 37]

Distribución de frecuencias para uhat1, observaciones 1-36

número de cajas = 7, media = 6,31594e-014, desv.típ.=2,83477

intervalo punto medio frecuencia rel acum.

-4,4236 - -2,7153 -3,5694 6 16,67% 22,22% ******

-2,7153 - -1,0069 -1,8611 4 11,11% 33,33% ***

-1,0069 - 0,70139 -0,15278 9 25,00% 58,33% ********

0,70139 - 2,4097 1,5556 8 22,22% 80,56% *******

2,4097 - 4,1181 3,2639 4 11,11% 91,67% ***

>= 4,1181 4,9722 3 8,33% 100,00% ***

Contraste de la hipótesis nula de distribución normal:

Chi-cuadrado(2) = 0,791 con valor p 0,67341

Análisis de Varianza:

Suma de cuadrados gl Media de cuadrados

Regresión 1005,75 1 1005,75

Residuo 273,222 34 8,03595

Total 1278,97 35 37,6168

R^2 = 1005,75 / 1278,97 = 0,786374

F(1, 34) = 1005,75 / 8,03595 = 125,156

[pic 38]

5.19. Table 5.10 gives annual data on the Consumer Price Index (CPI) and the Wholesale Price Index (WPI), also called Producer Price Index (PPI), for the U.S. economy for the period 1960–1999.

a. Plot the CPI on the vertical axis and the WPI on the horizontal axis. A priori, what kind of relationship do you expect between the two indexes? Why?

[pic 39]

b. Suppose you want to predict one of these indexes on the basis of the

other index. Which will you use as the regressand and which as the

regressor? Why?

c. Run the regression you have decided in b. Show the standard output.

Test the hypothesis that there is a one-to-one relationship between the

two indexes.

[pic 40]

d. From the residuals obtained from the regression in c, can you entertain

the hypothesis that the true error term is normally distributed?

Show the tests you use

. [pic 41]

Distribución de frecuencias para uhat1, observaciones 1-27

número de cajas = 7, media = -3,6843e-015, desv.típ.=4,26682

intervalo punto medio frecuencia rel acum.

-7,3153 - -4,4491 -5,8822 2 7,41% 11,11% **

-4,4491 - -1,5829 -3,0160 7 25,93% 37,04% *********

-1,5829 - 1,2833 -0,14982 6 22,22% 59,26% *******

1,2833 - 4,1494 2,7164 7 25,93% 85,19% *********

4,1494 - 7,0156 5,5825 3 11,11% 96,30% ***

>= 7,0156 8,4487 1 3,70% 100,00% *

Contraste de la hipótesis nula de distribución normal: