Question

1. Suppose you are testing a regression model for the presence of heteroskedasticity and the p-value is 0.00. Provide the null and alternative hypotheses, the rejection rule and interpret the result.

2. Suppose you are testing for serial correlation and using the Serial Correlation LM text where the p-value is 0.8415. Provide the null and alternative hypotheses, the rejection rule and interpret the result.

Answer 1

(a)

Question:

Suppose you are testing a regression model for the presence of heteroskedasticity and the p-value is 0.00. Provide the null and alternative hypotheses, the rejection rule and interpret the result.

By Breusch - Pagen test for heteroskedasticity in linear regression, we have:

H0: Null Hypothesis: . (There is no significant heteroskedasticity in linear regression,)

where

HA: Alternative Hypothesis: (At least one of the is not 0). (There is a significant heteroskedasticity in linear regression,)

The Test Statistic is given by:

= n R² k

where

n = the Sample Size

R = Coefficient of Determination based on a possible linear regression

k = number of independent variables.

The degrees of freedom is based on the number of independent variables instead of the sample size.

Rejection Region:

Reject H0 if calculated value of is greater than critical value of corresponding to significance level and the degrees of freedom which is based on the number of independent variables instead of the sample size.

Since p - value = 0.00 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there is a significant heteroskedasticity in linear regression,

(b)

Question:

Suppose you are testing for serial correlation and using the Serial Correlation LM text where the p-value is 0.8415. Provide the null and alternative hypotheses, the rejection rule and interpret the result.

H0: Null Hypothesis: (There is no serial correlation )

HA: Alternative Hypothesis: (At least one of the is not 0) (There is serial correlation ) (There is serial correlation ) (Claim)

Rejection Region:

Reject H0 if Calculated value of F is greater than critical value of F based on degrees of freedom and significance level .

Since p value = 0.8415 is greater than = 0.05, the difference is not significant. Fail to rejectnull hypothesis.

Conclusion:

The data support the claim that there is serial correlation