For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa. %3D
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
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![6. For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa.
7. In a linear regression model, if both dependent and explanatory variables are multiplied
by the same constant c, then the OLS solution of the new transformed model is multiplied
by c as well: 3
= c. Bold, where B is the OLS parameter estimate from the transformed
model.
i.i.d.
8. Consider a normal random variable X N(u, o?) and a corresponding random sample
{x1, ..., xn}, where n = 1138. An estimator of the mean u = E1 x; is downward
biased, however it is asymptotically unbiased.
9. In an Instrumental Variable regression we can check the assumption on instrument rele-
vance by considering a first stage regression. In particular, we should regress the instru-
ment on the endogenous variable and test the significance of the slope coefficient. If the
slope coefficient is significantly different from zero, we conclude that the instrument is
relevant.
10. Assume the population variance of a random variable is known, but the population mean
is not. When using a sample to estimate the population mean, if the sample size is doubled
then the variance of the distribution of the sample mean will be halved.
11. When testing for heteroscedasticity in a linear regression model it is preferable to use the
Breusch-Pagan test, as it is able to detect non-linear forms of heteroscedasticity and has
fewer parameters to estimate in the auxiliary regression, compared to the White test.
0 and E[f|2] = 0, then
12. In a bivariate regression model x; = d0 + d12i + Si, if cov(z, 5) = 0 and E[§|z] = 0, then
the OLS estimator d is an unbiased and consistent estimator of d1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0aa778ed-f124-4220-858b-6e3fee5e0b77%2F6c50f05a-458f-4951-b2b5-06dd0a7ac5dc%2Fbqo6kob_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa.
7. In a linear regression model, if both dependent and explanatory variables are multiplied
by the same constant c, then the OLS solution of the new transformed model is multiplied
by c as well: 3
= c. Bold, where B is the OLS parameter estimate from the transformed
model.
i.i.d.
8. Consider a normal random variable X N(u, o?) and a corresponding random sample
{x1, ..., xn}, where n = 1138. An estimator of the mean u = E1 x; is downward
biased, however it is asymptotically unbiased.
9. In an Instrumental Variable regression we can check the assumption on instrument rele-
vance by considering a first stage regression. In particular, we should regress the instru-
ment on the endogenous variable and test the significance of the slope coefficient. If the
slope coefficient is significantly different from zero, we conclude that the instrument is
relevant.
10. Assume the population variance of a random variable is known, but the population mean
is not. When using a sample to estimate the population mean, if the sample size is doubled
then the variance of the distribution of the sample mean will be halved.
11. When testing for heteroscedasticity in a linear regression model it is preferable to use the
Breusch-Pagan test, as it is able to detect non-linear forms of heteroscedasticity and has
fewer parameters to estimate in the auxiliary regression, compared to the White test.
0 and E[f|2] = 0, then
12. In a bivariate regression model x; = d0 + d12i + Si, if cov(z, 5) = 0 and E[§|z] = 0, then
the OLS estimator d is an unbiased and consistent estimator of d1.
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