Econometrics questions

A1) The residuals from a regression have the following signs:

(- - - -)(++)(- - - - - -)(++++)(- - -)(+++++)(- -)(++)

Test the null hypothesis of randomness by using a runs test and verify your conclusion both with: a. The confidence interval approach. b. The Swed-Eisenhart approach.

A2) You are given the following regression results:

1841.85 34 0.9946

(0.879) (-0.431) (0.067) (1.002)

1.358 0.764 - 3.451 255.1 ˆ

2

432







FnR

t

XXXY

Is there a problem with these results? If so, identify what the problem is. A3) Suppose you have calculated the following regression for 9 observations:

tttt uXXY 

33221 

The residuals from this regression are as follows:

t û -4 2 1 2 3 0 1 -3 -2

At the 5% level of significance, test for autocorrelation using the Durbin-Watson d test.

A4) Based on the simple regression iii

uXY  221

 on a data set of 11 observations, you are given the following data regarding the independent variable and the absolute value of the residuals:

Observation i

X 2

i

u

1 19.5 26.2

2 8.5 9.9

3 29.3 3.2

4 26.5 13.1

5 61.9 3.7

6 45.5 30.3

7 9.5 6.7

8 14.0 4.7

9 35.3 1.8

10 31.0 3.8

11 30.0 20.0

At the 5% level of significance, test whether heteroskedasticity exists by using Spearman’s rank correlation test.

A5) There are eight reasons for the presence of autocorrelation. List any five of them.