for query in above comment
7. In a simple regression model, suppose all of the assumptions of the classical linear regression...
012. (a) The ordinary least squares estimate of B in the classical linear regression model Yi = α + AXi + Ui ; i=1,2, , n and xi = Xi-K, X-n2Xī i- 1 Show that if Var(B-.--u , no other linear unbiased estimator of β n im1 can be constructed with a smaller variance. (All symbols have their usual meaning) 18
Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui. 1. [3 points] What are the assumptions of this model so that the OLS estimators are BLUE (best linear unbiased estimates)? 2. [4 points] Let βˆ and βˆ be the OLS estimators of β and β . Derive βˆ and βˆ. 12 1212 3. [2 points] Show that βˆ is an unbiased estimator of β .22
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
please show all work clearly ECN 702 Econometrics II HW2 Due: Jan 29 1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the term as in Assume cov (Xi, U.) = 0, E (Xn] = 0 and 티x?]-1. Is hisher estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [ui|X] of the real value X 0. It...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi , U) 0, E [Xn] O and E [x?-I . Is his/her estimate consistent for β,? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [u:|X0. It was discovered that we observe Xi with a measurement error wi instead of the real value X,...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
linear stat modeling & regression please , i need the solution for Q3, but i copy Q2 because you need info from Q2 in order to answer Q3. 2) Suppose you have multiple regression set up YxXBp The ridge regression estimator is given by Here, llell'-Σ.< where is a vector of Vik. a) Find the expectation and variance-covariance matrix of Bridge, when X'X is a diagonal matrix with each diagonal entry is eqal to. Com pare these variances with the...
I am looking for a solution for question number 2 ONLY with steps please, so I can find my mistake. 1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cov (Xi. Ui)s 0, E [Xn] = 0 and E [x?] = 1 . Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions 2. Assume the structural equation...