Study_questions_for_mt_1-2008

Study_questions_for_mt_1-2008 - Study Questions for Midterm...

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Study Questions for Midterm 1 ECG 561, Spring 2008 1. Consider two discrete random variables, X and Y. Their joint probability distribution is given in the table below: X 012 Y 01 / 30 0 10 1 / 3 1 / 3 a. Are X and Y independent? Support your answer. b. Calculate E(Y) and Var(Y). c. Plot E(Y|X) as a function of X. Label your diagram clearly. d. Calculate Cov(X,Y). 2. You have just calculated a simple linear regression with n observations. After you perform your analysis, you discover that there is one (x,y) pair that you overlooked; i.e., you really had n+1 observations available to you, but you only used n. It turns out that x n+1 = and y n+1 = : the overlooked data pair has x and y values equal to the sample means of the first n x's and y's. If you recalculate your regression results using all n+1 observations: (a) Will change? If so, how? (b) Will change? If so, how? (c) Will Var( ) change? If so, how? (d) Will the estimate of Var( ) change? If so, how? 3. Suppose that a researcher estimates a linear regression and is concerned about the validity of the assumption that E(u) = 0. To investigate, she calculates the sample mean of the residuals of the regression to see if it is likely that the population mean of the disturbances is non-zero. Comment on the advisability of the researcher’s procedure. 4. Consider a multiple regression with two independent variables: y i = β o + β 1 x 1i + β 2 x 2i + u i . (a) State the two conditions that imply that the least squares multiple regression coefficient on x 1 , , will equal the simple coefficient from a least squares regression of y on x 1 , .
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Study_questions_for_mt_1-2008 - Study Questions for Midterm...

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