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4. Suppose you are interested in estimating the ceteris paribus relationship between final exam scores (y) and class attendance (x1). You can also collect data on two control variables, x2 and x3, which could be GPA and SAT scores. Let B1 be the bivariate regression estimate on x1 only and B represent the estimate from the full regression with all controls. (a) If class attendance is highly correlated with both controls, and both controls have a large effect on y, would you expect the two estimates to be similar or very different? Why? (b) If class attendance is uncorrelated with the two controls, but the two controls are highly correlated with each other, will the two estimates tend to be similar or different? Why? (c) If class attendance is highly correlated with the two controls, and the two controls have very small effects on y, do we expect the two estimates to be similar or different on average? Why?

4. Suppose you are interested in estimating the ceteris paribus relationship between final exam scores (y) and class attendance (x1). You can also collect data on two control variables, x2 and x3, which could be GPA and SAT scores. Let B1 be the bivariate regression estimate on x1 only and B represent the estimate from the full regression with all controls. (a) If class attendance is highly correlated with both controls, and both controls have a large effect on y, would you expect the two estimates to be similar or very different? Why? (b) If class attendance is uncorrelated with the two controls, but the two controls are highly correlated with each other, will the two estimates tend to be similar or different? Why? (c) If class attendance is highly correlated with the two controls, and the two controls have very small effects on y, do we expect the two estimates to be similar or different on average? Why?

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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4. Suppose you are interested in estimating the ceteris paribus relationship between final exam scores (y) and class attendance (x1). You can also collect data on two control variables, x2 and x3, which could be GPA and SAT scores. Let B1 be the bivariate regression estimate on x1 only and B1 represent the estimate from the full regression with all controls. (a) If class attendance is highly correlated with both controls, and both controls have a large effect on y, would you expect the two estimates to be similar or very different? Why? (b) If class attendance is uncorrelated with the two controls, but the two controls are highly correlated with each other, will the two estimates tend to be similar or different? Why? (c) If class attendance is highly correlated with the two controls, and the two controls have very small effects on y, do we expect the two estimates to be similar or different on average? Why?
Transcribed Image Text:4. Suppose you are interested in estimating the ceteris paribus relationship between final exam scores (y) and class attendance (x1). You can also collect data on two control variables, x2 and x3, which could be GPA and SAT scores. Let B1 be the bivariate regression estimate on x1 only and B1 represent the estimate from the full regression with all controls. (a) If class attendance is highly correlated with both controls, and both controls have a large effect on y, would you expect the two estimates to be similar or very different? Why? (b) If class attendance is uncorrelated with the two controls, but the two controls are highly correlated with each other, will the two estimates tend to be similar or different? Why? (c) If class attendance is highly correlated with the two controls, and the two controls have very small effects on y, do we expect the two estimates to be similar or different on average? Why?
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