I AM STRUGLING WITH THESE QUESTIONS PLEASE HELP ME SOLVE THEM 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 B. The usual inference techniques, based on the t and χ2 distributions, are no longer valid.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. MY ANSWERS 1. The Jarque-Bera test is a goodness-of-fit test to see if the sample data follows normal distribution. The test uses skewness and kurtosis. JB=n6S2+14K-32 where, S denotes skewness, K denotes Kurtosis, n denotes the number of observations. From the given information, i. S=-0.93726 ii. K=1.561158 iii. The number of observations is not provided. Substituting all the values in the stated formula, the JB test statistic can be obtained. JB=N6(-0.93726)2+14(1.561158)-32 I cant seem to find a suitable answe please assist me in these 4 questions Addiitional Information from part 2 Sarah wants to estimate the relationship between individual earnings in the labour market (earn) and years of education achieved (educ). She collects data from a sample of 122 individuals on their monthly salaries (Y), measured in rands, and education levels (X), measured in years of education. Based on these data, she derives the following estimates: ∑XY=41421943.8 ∑X2=15472 ∑X=1242 ∑Y=3401031

I AM STRUGLING WITH THESE QUESTIONS PLEASE HELP ME SOLVE THEM 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. MY ANSWERS 1. The Jarque-Bera test is a goodness-of-fit test to see if the sample data follows normal distribution. The test uses skewness and kurtosis. JB=n6S2+14K-32 where, S denotes skewness, K denotes Kurtosis, n denotes the number of observations. From the given information, i. S=-0.93726 ii. K=1.561158 iii. The number of observations is not provided. Substituting all the values in the stated formula, the JB test statistic can be obtained. JB=N6(-0.93726)2+14(1.561158)-32 I cant seem to find a suitable answe please assist me in these 4 questions Addiitional Information from part 2 Sarah wants to estimate the relationship between individual earnings in the labour market (earn) and years of education achieved (educ). She collects data from a sample of 122 individuals on their monthly salaries (Y), measured in rands, and education levels (X), measured in years of education. Based on these data, she derives the following estimates: ∑XY=41421943.8 ∑X2=15472 ∑X=1242 ∑Y=3401031

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.1: Functions Of Several Variables

Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...

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I AM STRUGLING WITH THESE QUESTIONS PLEASE HELP ME SOLVE THEM

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.

MY ANSWERS

The Jarque-Bera test is a goodness-of-fit test to see if the sample data follows normal distribution. The test uses skewness and kurtosis.

JB=n6S2+14K-32

where, S denotes skewness, K denotes Kurtosis, n denotes the number of observations.

From the given information,

i. S=-0.93726

ii. K=1.561158

iii. The number of observations is not provided.

Substituting all the values in the stated formula, the JB test statistic can be obtained.

JB=N6(-0.93726)2+14(1.561158)-32

I cant seem to find a suitable answe please assist me in these 4 questions

Addiitional Information from part 2

Sarah wants to estimate the relationship between individual earnings in the labour market (earn) and years of education achieved (educ). She collects data from a sample of 122 individuals on their monthly salaries (Y), measured in rands, and education levels (X), measured in years of education.

Based on these data, she derives the following estimates:

∑XY=41421943.8
∑X2=15472
∑X=1242
∑Y=3401031

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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