Please solve it ASAP before 10:30, will thump up, thank you 2. (Serial Correlation) Consider the following time series regression modelYt = Bo + B1t +,t = 1,..,TEt = Ut + pUt-1,PE (0, 1),where x and ut are i.i.d. over t and are independent of each other. Assume E[u] = 0, E[u?] = o². Let B1be the OLS estimator of B1 from regressing yt on xt (with an intercept). For simplicity, in the following weassume {rt :1 2.(b) Let i = -2=1 Tt. Use your answer to part (a) to show thatT.T.vE(a; – 1)6 = (1+ p²)o² E(# – #)² + 2po² (a - )(x1-1 – ).Vt=1t=1t=2(Hint: use the fact that for generic random variables z1, VIE-1 21] = E V[zı]+2E-2 E Cou[zt, 21-e).)t%3D2

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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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Consider the fitted values from a simple linear regression model with intercept: yˆ = 5 + 6x. Assume that the total number of observations is n = 302. In addition, the R-squared of the regression is R2 = 0.6 and Pn i=1(xi − x¯) 2 = 15, where ¯x is the sample mean of x. Under the classical Gauss-Markov assumptions, a) What is the standard error of the estimated slope coefficient?
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Consider the fitted values from a simple linear regression model with intercept: yˆ = 5 + 6x. Assume that the total number of observations is n = 302. In addition, the R-squared of the regression is R2 = 0.6 and Pn i=1(xi − x¯) 2 = 15, where ¯x is the sample mean of x. Under the classical Gauss-Markov assumptions standard error of the estimated slope coefficient = 0.0365 value of the t-statistic for the null hypothesis H0 : the slope coefficient is equal to 0 versus H1 : the slope coefficient is different from 0 = 164.3836 What is the value of the F-statistic for the null hypothesis H0 : the slope coefficient is equal to 0 versus H1 : the slope coefficient is different from 0? Do the p-values of the t- and F-tests differ from each other? Justify your answer.

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