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2. Imagine that, instead of estimating y = XB+, you estimate y = Zy+ & where Z = XP with P being a nonsingular matrix that transforms the columns of X. For example, you can imagine that P would change the measurement units of some variables in X (e.g. going from cm to meters). a) Show that the OLS estimator of y will equal P-¹b where b is the OLS estimator of B. b) Show that the R-squared of the two regressions will be identical.

2. Imagine that, instead of estimating y = XB+, you estimate y = Zy+ & where Z = XP with P being a nonsingular matrix that transforms the columns of X. For example, you can imagine that P would change the measurement units of some variables in X (e.g. going from cm to meters). a) Show that the OLS estimator of y will equal P-¹b where b is the OLS estimator of B. b) Show that the R-squared of the two regressions will be identical.

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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2. Imagine that, instead of estimating y = XB + ɛ, you estimate y = Zx + ɛ where Z = XP with P being a nonsingular matrix that transforms the columns of X. For example, you can imagine that P would change the measurement units of some variables in X (e.g. going from cm to meters). a) Show that the OLS estimator of y will equal P-'b where b is the OLS estimator of ß. b) Show that the R-squared of the two regressions will be identical.
Transcribed Image Text:2. Imagine that, instead of estimating y = XB + ɛ, you estimate y = Zx + ɛ where Z = XP with P being a nonsingular matrix that transforms the columns of X. For example, you can imagine that P would change the measurement units of some variables in X (e.g. going from cm to meters). a) Show that the OLS estimator of y will equal P-'b where b is the OLS estimator of ß. b) Show that the R-squared of the two regressions will be identical.
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