(E3) Consider the following population regression model Y 105X1 v U -10 + 10X1 + u...
PLEASE SHOW ALL THE WORK!
(E3) Consider the following population regression model Y 105X1 v U -10 + 10X1 + u where X1 and u are two independently-distributed standard normal random variables (i.e. such that cov(X1,u) 0) EKLEKj, EKs], etc.) of a standard What is cov(Χι, ν)? (Hint: The normal random variable are all zero). (ii) odd moments (e.g.
(E3) Consider the following population regression model Y 105X1 v U -10 + 10X1 + u where X1 and u are two independently-distributed standard normal random variables (i.e. such that cov(X1,u) 0) (v) Prove algebraically that a1 is a biased estimator of the true effect of X1 on Y from the population regression model, Y 10 5X. Derive an analytic expression for the degree of bias.
PLEASE SHOW EVERY STEP! HOW DO YOU GET THE RESULT
(E3) Consider the following population regression model Y 105X1 v U -10 + 10X1 + u where X1 and u are two independently-distributed standard normal random variables (i.e. such that cov(X1,u) 0) (i) Given that X1 and u are distributed N(0,1), what is E[v]?
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct? a. When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. b....
1. Consider the following regression model with a single endogenous variable, ya : and given the reduced from for x: where z and are exogenous variables in the sense that cov(u,21) = cov(11,2 ) = 0 and cov(v,21) = cov(ng) = 0 (i.e., both zi and z2 are uncorrelated with u and v, and u is uncorrelated with v) (a) By substituting x into the equation for y, we obtain the reduce formed equation for y: Find the a in...
Q.8 In a regression model, the assumptions of the method of least squares include: [I] Relationship between x and y is linear [II] the values of X are fixed (non-random) [III] the error terms must be correlated with each other [IV] X is independent of Y [V] the error term is normal and is identically and independently distributed about the mean of zero [VI] the error term is normal but non random a. I, II, V b. II, III, VI...
a,b,c,d
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume that the true model satisfies all five standard assumptions of a simple regression model discussed in class. (a) Does the regression model we are running satisfy the zero conditional mean assumption? (b) Find the expected value of A (given X values). (e) Does the regression model we are running satisfy homoscedasticity? d) Find the variance of pi (given X...
2. Consider the following model: y = XB + u where y is a (nx1) vector containing observations on the dependent variable, B = Bi , B X is a (n x 3) matrix. The first column of X is a column of ones whilst the second and third columns contain observations on two explanatory variables (x and x2 respectively). u is (n x 1) vector of error terms. The following are obtained: 1234.7181 1682.376 7345.581 192.0 259.6 1153.1) X'X...
7 Consider the following regression output involving the variables y and, rı, r2. (note log is the natural logarithm as usual) 4.12 0.88 r Model A: Model B: log(y)0.34 0.14 + 0.001 2 Model C: logly)2011.4 log()0.02 r2 0.06 Model D: Model E: y = 5.4 + 0.82i --3.4 55.1 log(0.020 2 + 1.2r2 0.2 (1x2) Ceteris Paribus: (a) In Model A: If x1 increases 6 to 8 by 2 units, then the predicted change in y is Δy =...