Derive the OLS estimator \hat{β}₀ in the regression model yi=β₀+ui. Show all of the steps in your derivation.
Taking the yellow parts below as a model to solve the question above. Thank you!!!!!!!! Prove that the OLS estimator As for β in the linear regression model is consistent Let's first show that the OLS estimator is consistent Recall the result for β LS-(Lil Xix;厂E-1 xīYi Using Yi = X(B* + ui By the WLLN Assuming that E(X,X is non-negative definite (so that its inverse exists) and using Slutsky's theorem It follows In words: ßOLs converges in probability to...
1. Consider a regression model Yi = x;ß +ei, i = 1,...,n. You estimate this model using the OLS estimator. (a) Present and discuss assumptions for the OLS estimation.
Question 1 Consider the following model Yi = B.z; + u (a) Derive the OLS estimator of B, B. (6 marks] (b) Show that is unbiased. [9 marks] (c) Find the variance of B. [7 marks]
Question 1 Consider the following model Yi = Bx; +ui (a) Derive the OLS estimator of B, ß. (6 marks] (b) Show that B is unbiased. (9 marks] (c) Find the variance of ß. [7 marks] -r.pdf
Consider the zero intercept model given by Yi = B1Xi + ei (i=1,…,n) with the ei normal, independent, with variance sigma^2. For this mode (i) find the sum of (Yi –Yi-hat). (ii) find the sum of (Yi – Yi-hat)Xi. (iii) find the estimator of the error variance, sigma^2. (iv) is the estimator of the error variance biased?
Question 2 (10 points) You are given the following model y-put ei. Consider two alternative estimators of β, b2xvix? and b = Zy/X 1. Which estimator would you choose and why if the model satisfies all the assumptions of classical regression? Prove your results. (4 points) 2. Now suppose that var(y)-hxi, where h is a positive constant (a) Obtain the correct variance of the OLS estimator. (2 points) (b) Show that the BLU estimator is now 6. Derive its variance....
Consider the linear model: Yi = α0 + α1(Xi − X̄) + ui. Find the OLS estimators of α0 and α1. Compare with the OLS estimators of β0 and β1 in the standard model discussed in class (Yi = β0 + β1Xi + ui). Consider the linear model: Yį = ao + Q1(X; - X) + Ui. Find the OLS estimators of do and a1. Compare with the OLS estimators of Bo and B1 in the standard model discussed in...
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
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ), β-(A ,A, β), and σ2 are unknown parameters, zı, known constants with x1 +... + Xm-Tm+1 + +xn0 , zn are 1, write the model in vector form as Y = Xß+ε describing the entries in the matrix X. 2, Determine the least squares estimator β of β. Exercise5 Consider a linear model with n -2m in which...