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 multipliedby the same constant c, then the OLS solution of the new transformed model is multipliedby c as well: 3= c. Bold, where B is the OLS parameter estimate from the transformedmodel.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 downwardbiased, 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 theslope coefficient is significantly different from zero, we conclude that the instrument isrelevant.10. Assume the population variance of a random variable is known, but the population meanis not. When using a sample to estimate the population mean, if the sample size is doubledthen 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 theBreusch-Pagan test, as it is able to detect non-linear forms of heteroscedasticity and hasfewer parameters to estimate in the auxiliary regression, compared to the White test.0 and E[f|2] = 0, then12. In a bivariate regression model x; = d0 + d12i + Si, if cov(z, 5) = 0 and E[§|z] = 0, thenthe OLS estimator d is an unbiased and consistent estimator of d1.

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MATLAB: An Introduction with Applications

6th Edition

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Author:Amos Gilat

Publisher:Amos Gilat

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1. Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.4, standard error for the coefficient of z is 0.01, and the sample size is 20. Based on this information, find out whether labor cost is a statistically significant variable using an appropriate statistical test.
Consider the following regression model Yt = β0 + β1 Ut + β2 Vt + β3 Wt + β4Xt + ∈t , where U, V, W, X and Y are economic variables observed from t = 1, . . . , 75, β0 , . . . , β4 are the model parameters and ∈t is the random disturbance term satisfying the classical assumptions. Ordinary Least Squares (OLS) is used to estimate the parameters, producing the following estimated model: Yt = 1.115 + 0.790*Ut − 0.327*Vt + 0.763*Wt + 0.456*Xt (0.405) (0.178) (0.088) (0.274) (0.017) where standard errors are given in parentheses, the R-squared = 0.941, the Durbin-Watson statistic is DW = 1.907 and the residual sum of squares is RSS = 0.0757. In answering this question, use the 5% level of signiﬁcance for any hypothesis tests that you are asked to perform, state clearly the null and al- ternative hypotheses that you are testing, the test statistics that you are using and interpret the decisions that you make.…
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For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa. %3D