Question

Suppose for a multiple regression on just 5 observations you are given the following portion of an excel regression output:

RESIDUAL OUTPUT

Observation	Predicted y(hat)	Residuals
1	73.61	0.39
2	93.03	-1.03
3	58.97	-0.97
4	85.21	-0.21
5	78.18	1.82

Test the model for autocorrelation at a 10% level of significance.

Test the model for heteroskedasticity using a level of significance of 5%

Answer 1

The details solution given below.

For autocorrelation

The Hypotheses for the Durbin Watson test are:

H0 = no first order autocorrelation.
H1 = first order correlation exists.

d = 6.7185 / 5.5104

d = 1.21924

From the value of d we can say that 0 to <2 is positive autocorrelation at given level of significance.

For Heteroskedasticiy

Test the model of Heteroskedasticity using the graphical method there is no prior information about the nature of heteroscedasticity.

We can say that there is no any pattern or not constant pattern between two variables we can't say at in present data.

By using the Breusch Pagan Test (B-P test) for Heterosckdasticiy

• The test statistic is the result of the coefficient of determination of the auxiliary regression in Step 2 and sample size n {\displaystyle n\,} with:

n=5

The test statistic is LM = ESS/2

=ei^2 /2

= 5.5104 / 5 = 1.10208

critical value chisq at 5% = 0.710723

Ho: There is no heteroskedasticiy in the data

H1: There is heteroskedasticity in the data

Conclusion: test statistic value is greater than critical value then Reject Ho

i.e. There is heteroscedasticity in above data at 5% of level of significance.