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1. The t test is sometimes invalid in small samples because the t statistic does not have a t distribution when there exists heteroskedasticity in error terms. However, we can still use the t-test even if the error terms are heteroskedastic because we can eliminate heteroskedasticity from error term by GLS (generalized least square) estimator. 2. Suppose a regression of Y on X is run and the t-statistic for testing H, : B =0 has a p-value of 0.0295 associated with it. Using a 5% level of significance, the null hypothesis should be rejected. 3. If the correlation between X and Y is 0.9, then the R2 value for a simple linear regression of Y on X will be 90%.

1. The t test is sometimes invalid in small samples because the t statistic does not have a t distribution when there exists heteroskedasticity in error terms. However, we can still use the t-test even if the error terms are heteroskedastic because we can eliminate heteroskedasticity from error term by GLS (generalized least square) estimator. 2. Suppose a regression of Y on X is run and the t-statistic for testing H, : B =0 has a p-value of 0.0295 associated with it. Using a 5% level of significance, the null hypothesis should be rejected. 3. If the correlation between X and Y is 0.9, then the R2 value for a simple linear regression of Y on X will be 90%.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. The t test is sometimes invalid in small samples because the t statistic does not have a t distribution when there exists heteroskedasticity in error terms. However, we can still use the t-test even if the error terms are heteroskedastic because we can eliminate heteroskedasticity from error term by GLS (generalized least square) estimator. 2. Suppose a regression of Y on X is run and the t-statistic for testing H,: B, = 0 has a p-value of 0.0295 associated with it. Using a 5% level of significance, the null hypothesis should be rejected. 3. If the correlation between X and Y is 0.9, then the R value for a simple linear regression ofY on X will be 90%. 4. Even though least squares estimators and maximum likelihood estimators involve different estimation procedures, in the simple linear regression estimation, they provide the exact same estimators for Bo. Bi and o 5. In sufficiently large samples, regression coefficients will always be significantly different from zero 6. OLS procedure will generate unbiased but inefficient estimator in the presence of serial correlation.
Transcribed Image Text:1. The t test is sometimes invalid in small samples because the t statistic does not have a t distribution when there exists heteroskedasticity in error terms. However, we can still use the t-test even if the error terms are heteroskedastic because we can eliminate heteroskedasticity from error term by GLS (generalized least square) estimator. 2. Suppose a regression of Y on X is run and the t-statistic for testing H,: B, = 0 has a p-value of 0.0295 associated with it. Using a 5% level of significance, the null hypothesis should be rejected. 3. If the correlation between X and Y is 0.9, then the R value for a simple linear regression ofY on X will be 90%. 4. Even though least squares estimators and maximum likelihood estimators involve different estimation procedures, in the simple linear regression estimation, they provide the exact same estimators for Bo. Bi and o 5. In sufficiently large samples, regression coefficients will always be significantly different from zero 6. OLS procedure will generate unbiased but inefficient estimator in the presence of serial correlation.
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