Suppose a data set consists of N observations. The outcome variable of interests is y, and...

 

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Suppose a data set consists of N observations. The outcome variable of interests is y, and the explanatory variables are denoted by X = [X1, X2]. There are K, variables in X, and K2 variables in X2. (Put it differently, X, is a N x K1 matrix, while X, is a N x K2 matrix.) Do the following four procedures produce the same value for the least squares coefficients on X2? (a) Regress y on both X1 and X2. (b) Regress the residuals from a regression of y on X, on the residuals (column by column) of regressions of X, on X1. (c) Same as (b), but do not transform y. (d) Same as (b), but do not transform X2. You may justify your answers based on theoretical proofs or Monte Carlo simulations. For simplicity, you may assume that K1 = K2 = 1. If you opt for the approach of Monte Carlo simulations, attach the Stata codes and outputs. Suppose a data set consists of N observations. The outcome variable of interests is y, and the explanatory variables are denoted by X = [X1, X2]. There are K, variables in X, and K2 variables in X2. (Put it differently, X, is a N x K1 matrix, while X, is a N x K2 matrix.) Do the following four procedures produce the same value for the least squares coefficients on X2? (a) Regress y on both X1 and X2. (b) Regress the residuals from a regression of y on X, on the residuals (column by column) of regressions of X, on X1. (c) Same as (b), but do not transform y. (d) Same as (b), but do not transform X2. You may justify your answers based on theoretical proofs or Monte Carlo simulations. For simplicity, you may assume that K1 = K2 = 1. If you opt for the approach of Monte Carlo simulations, attach the Stata codes and outputs.

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1 SS total is the sum of the squares due to the absolute difference It considers all var... View the full answer