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 3Question 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 B. The usual inference techniques, based on the t and χ2 distributions, are no longer valid.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.

Since, the question to be answered is not specified, we'll be answering the first question only.…

Answered: The JB test-statistic is given by ?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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