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Suppose we want to predict a continuous response Y. The true conditional expectation of Y is given by, E(Y | X, Z) = = Bo+ B1X + B2Z Here Z is a continuous but an unobserved predictor and X is an observed continuous predictor. From the real life data we can only observe y₁, 92, ..., Yn and x1, x2,..., n and fit the following model, ŷi = Bo + ₁x₂ Then answer the following problems, (a) The estimator 3₁ is a biased estimator. Calculate the bias of the estimator. That is calculate 3₁-E (3₁). Show the detailed derivations. (b) Calculate the Var(81 | X, Z) using the fitted model under the constant variance assumption. Show the detailed derivations.

Suppose we want to predict a continuous response Y. The true conditional expectation of Y is given by, E(Y | X, Z) = = Bo+ B1X + B2Z Here Z is a continuous but an unobserved predictor and X is an observed continuous predictor. From the real life data we can only observe y₁, 92, ..., Yn and x1, x2,..., n and fit the following model, ŷi = Bo + ₁x₂ Then answer the following problems, (a) The estimator 3₁ is a biased estimator. Calculate the bias of the estimator. That is calculate 3₁-E (3₁). Show the detailed derivations. (b) Calculate the Var(81 | X, Z) using the fitted model under the constant variance assumption. Show the detailed derivations.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose we want to predict a continuous response Y. The true conditional expectation of Y is given by, E(Y | X, Z) = Bo+B1X+B2Z Here Z is a continuous but an unobserved predictor and X is an observed continuous predictor. From the real life data we can only observe y₁, y2, ,..., Yn and x₁, x2,..., n and fit the following model, ŷi = ß0 + Â₁xi Then answer the following problems, (a) The estimator B₁ is a biased estimator. Calculate the bias of the estimator. That is calculate B₁ - E₁). Show the detailed derivations. (b) |Calculate the Var(8₁ | X, Z) using the fitted model under the constant variance assumption. Show the detailed derivations.
Transcribed Image Text:Suppose we want to predict a continuous response Y. The true conditional expectation of Y is given by, E(Y | X, Z) = Bo+B1X+B2Z Here Z is a continuous but an unobserved predictor and X is an observed continuous predictor. From the real life data we can only observe y₁, y2, ,..., Yn and x₁, x2,..., n and fit the following model, ŷi = ß0 + Â₁xi Then answer the following problems, (a) The estimator B₁ is a biased estimator. Calculate the bias of the estimator. That is calculate B₁ - E₁). Show the detailed derivations. (b) |Calculate the Var(8₁ | X, Z) using the fitted model under the constant variance assumption. Show the detailed derivations.
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