One is interested in the ceteris paribus relationship between the dependent variable y, and theexplanatory variable ₁1. For this, one collects data on two control variables Xi2 and Xiz and runstwo LS regressions.Regression 1: yi = B₁x₁1 + UiRegression 2: y = B₁xil+ B₂x₁2 + B3x13 + EiLet ₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁in Regression 2. Assume that the true model is given by Regression 2 and that all variables arecentered.a) Would you expect a difference between ₁ and ₁ when is highly correlated with 2and 3 and the partial effects of xi2 and xi3 on yi are also high?b) Would you expect a difference between ₁ and 3₁ when ₁ has almost no correlation withand Xi3 but X2 and 3 are highly correlated?Xi2c) Which of the two estimators is more efficient if x₁1 is highly correlated with 2 and 13,and Xiz have small partial effects on yi?but i2d) Which of the two estimators is more efficient if x₁1 is almost uncorrelated with 2 and 13,wherein ₁2 and 13 have large partial effects on yi and xi2 and is are highly correlated?

a) When 21 is highly correlated with X12 and X 13, and the partial effects of X12 and X13 on yi are…

One is interested in the ceteris paribus relationship between the dependent variable y; and the explanatory variable ₁1. For this, one collects data on two control variables 2 and 3 and runs two LS regressions. Regression 1: yi = Buil+ui Regression 2: yi = B1x1 + B₂x2 + 3x i3 + Ei Let B₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. b) would you expect a difference between ₁ and 3₁ when ₁₁ has almost no correlation with Xi2 and and 3 are highly correlated? but 2 Xiz a) Would you expect a difference between ₁ and ₁ when ₁₁ is highly correlated with 2 and 3 and the partial effects of xi2 and is on y, are also high?

One is interested in the ceteris paribus relationship between the dependent variable y; and the explanatory variable ₁1. For this, one collects data on two control variables 2 and 3 and runs two LS regressions. Regression 1: yi = Buil+ui Regression 2: yi = B1x1 + B₂x2 + 3x i3 + Ei Let B₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. b) would you expect a difference between ₁ and 3₁ when ₁₁ has almost no correlation with Xi2 and and 3 are highly correlated? but 2 Xiz a) Would you expect a difference between ₁ and ₁ when ₁₁ is highly correlated with 2 and 3 and the partial effects of xi2 and is on y, are also high?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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