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Question 1 Consider the following model Yi = B.z; + u (a) Derive the OLS estimator...
Question 1 Consider the following model Yi = Bx; +ui (a) Derive the OLS estimator of...
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
Derive the OLS estimator β₀ in the regression model yi=β₀+ui.
Derive the OLS estimator \hat{β}₀ in the regression model yi=β₀+ui. Show all of the steps in your derivation.
4. Consider the model yi-β +82i + ei. Find the OLS estimator for β.
4. Consider the model yi-β +82i + ei. Find the OLS estimator for β.
Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui....
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
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we ca...
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we call it regression through the origin. Consider a population model Y- Au + βίχ + u and we estimate an OLS regression model through the origin: Y-β¡XHi (note that the true intercept parameter Bo is not necessarily zero). (i) Under assumptions SLR.1-SLR.4, either use the method of moments or minimize the SSR to show that the βί-1-- ie1 (2) Find E(%) in terms...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo +...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo + Bicite and the model satisfies the Gauss-Markov conditions. Answer the following questions: (a) What assumption in addition to the Gauss-Markov assumptions is required to estimate the model? (b) Show that in general, b is a biased estimator of B1. (c) Outline the special condition(s) under which b is an unbiased estimator of B1.
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) W...
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...
3. Let y = (yi..... Yn) be a set of re- sponses, and consider the linear...
3. Let y = (yi..... Yn) be a set of re- sponses, and consider the linear model y= +E, where u = (1, ..., and e is a vector of zero mean, uncorrelated errors with variance o'. This is a linear model in which the responses have a constant but unknown mean . We will call this model the location model. (a) If we write the location model in the usual form of the linear model y = X 8+...
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 al...
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....
Please provide step by step solutions and explanations for below questions 1. Derive the OLS estimator...
Please provide step by step solutions and explanations for below
questions
1. Derive the OLS estimator for B1 2. Prove that it is unbiased 3. Given the data below Obs y 25 X 2 1 5 2 14 1 4 38 -2 4 3 7 4 23 50 0 5 Compute B using algebra. In other words you are god and you observe u. Now use your ols estimator, as a human who does not observe u, to compute B....
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
4. Consider the model yi-β +82i + ei. Find the OLS estimator for β.
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we call it regression through the origin. Consider a population model Y- Au + βίχ + u and we estimate an OLS regression model through the origin: Y-β¡XHi (note that the true intercept parameter Bo is not necessarily zero). (i) Under assumptions SLR.1-SLR.4, either use the method of moments or minimize the SSR to show that the βί-1-- ie1 (2) Find E(%) in terms...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo + Bicite and the model satisfies the Gauss-Markov conditions. Answer the following questions: (a) What assumption in addition to the Gauss-Markov assumptions is required to estimate the model? (b) Show that in general, b is a biased estimator of B1. (c) Outline the special condition(s) under which b is an unbiased estimator of B1.
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...
3. Let y = (yi..... Yn) be a set of re- sponses, and consider the linear model y= +E, where u = (1, ..., and e is a vector of zero mean, uncorrelated errors with variance o'. This is a linear model in which the responses have a constant but unknown mean . We will call this model the location model. (a) If we write the location model in the usual form of the linear model y = X 8+...
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....
Please provide step by step solutions and explanations for below
questions
1. Derive the OLS estimator for B1 2. Prove that it is unbiased 3. Given the data below Obs y 25 X 2 1 5 2 14 1 4 38 -2 4 3 7 4 23 50 0 5 Compute B using algebra. In other words you are god and you observe u. Now use your ols estimator, as a human who does not observe u, to compute B....
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