The JB test-statistic is given by  ?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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For the residuals derived from Sarah's regression, skewness (S) equals -0.93726 and kurtosis (K) equals 1.561158. Conduct the Jarque-Bera test of normality at α=0.01.

Starting with the following null and alternative hypotheses:

H0= Residuals are normally distributed.
H1= Residuals are not normally distributed.

part 3
Question 1 
 

The JB test-statistic is given by  ?

 
Question 2 
 
The χ2 statistic is given by?.  
Question 3
 
  •  A. Since the JB statistic is greater than the χ2 statistic, H0 can be rejected. Therefore the alternative hypothesis is assumed. The residuals are not normally distributed.
  •  B. Since the JB statistic is greater than the χ2 statistic, H0 can be rejected. Therefore the null hypothesis is assumed. The residuals are normally distributed.
  •  C. Since the JB statistic is less than the χ2 statistic, H0 cannot be rejected. Therefore the null hypothesis is assumed. The residuals are normally distributed.
  •  D. Since the JB statistic is less than the χ2 statistic, H0 can be rejected. Therefore the null hypothesis is assumed. The residuals are not normally distributed.


Question 4 
What are the implications for the model given the result of the JB test above?
 
  •  A. The CLRM assumptions no longer hold and therefore none of the OLS properties hold.
  •  B. The usual inference techniques, based on the t and χ2 distributions, are no longer valid.
  •  C. There are no implications, the model is interpreted as normal.
  •  D. The Z-distribution table should now be used for inference.
  •  E. The error terms are heteroscedastic, thus the estimators are not efficient.
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