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In the least squares regression of y on a constant and X, to compute the regression coefficients on X, we can first transform y to deviations from the mean ỹ and, likewise, transform each column of X to deviations from the respective column mean; second, regress the transformed y on the transformed X without a constant. Do we get the same result if we only transform y? What if we only transform X?

In the least squares regression of y on a constant and X, to compute the regression coefficients on X, we can first transform y to deviations from the mean ỹ and, likewise, transform each column of X to deviations from the respective column mean; second, regress the transformed y on the transformed X without a constant. Do we get the same result if we only transform y? What if we only transform X?

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. In the least squares regression of y on a constant and X, to compute the regression coefficients on X, we can first transform y to deviations from the mean y and, likewise, transform each column of X to deviations from the respective column mean; second, regress the transformed y on the transformed X without a constant. Do we get the same result if we only transform y? What if we only transform X?
Transcribed Image Text:2. In the least squares regression of y on a constant and X, to compute the regression coefficients on X, we can first transform y to deviations from the mean y and, likewise, transform each column of X to deviations from the respective column mean; second, regress the transformed y on the transformed X without a constant. Do we get the same result if we only transform y? What if we only transform X?
Bo = = Y-8₁X n Σ(X₁-X)(Yi-Y) n Σ(x; − x)2 i=1 i=1 n = Σ (Ŷ₁ - Y)² = B₁(x₁ - x)² i=1 SST = (Y₁ - Y)² SSR = ₂². R² = SSE = SST = 1- SSR SST Var() = 0² (²) + Var(8₁) = 0² Σ(x-x)2
Transcribed Image Text:Bo = = Y-8₁X n Σ(X₁-X)(Yi-Y) n Σ(x; − x)2 i=1 i=1 n = Σ (Ŷ₁ - Y)² = B₁(x₁ - x)² i=1 SST = (Y₁ - Y)² SSR = ₂². R² = SSE = SST = 1- SSR SST Var() = 0² (²) + Var(8₁) = 0² Σ(x-x)2
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