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correlation is then given by 8XY rXY 8x8Y nd sy are the sample standard deviations of X and Y, respective that the regression R² in the regression of Y on X is the squa tion between X and Y. That is, show that R? = r{y. hat the R2 from the regression of Y on X is the same as the R2 chat Sy B1 = rxy Sx ss of OLS estimators chat beta, can be written as: :E(X; – X)u;

correlation is then given by 8XY rXY 8x8Y nd sy are the sample standard deviations of X and Y, respective that the regression R² in the regression of Y on X is the squa tion between X and Y. That is, show that R? = r{y. hat the R2 from the regression of Y on X is the same as the R2 chat Sy B1 = rxy Sx ss of OLS estimators chat beta, can be written as: :E(X; – X)u;

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. The sample covariance of two random variables X and Y in a sample of size n is given by n 1 SXY = E(X; - X)(Y; – Ỹ). п — 1 i=1 The sample correlation is then given by SXY rXY = SxSy where sx and sy are the sample standard deviations of X and Y, respectively. (a) Show that the regression R? in the regression of Y on X is the squared value of the sample correlation between X and Y. That is, show that R2 = ry. (b) Show that the R2 from the regression of Y on X is the same as the R2 from the regression of X on Y. (c) Show that Sy = rXY 5. Unbiasedness of OLS estimators (a) Show that beta, can be written as: - iE (X; – X)u; (X; - X)2 (b) Use the result from (a) to show that B1 is an unbiased estimator of B1. (c) Show that Bo is an unbiased estimator of Bo.
Transcribed Image Text:4. The sample covariance of two random variables X and Y in a sample of size n is given by n 1 SXY = E(X; - X)(Y; – Ỹ). п — 1 i=1 The sample correlation is then given by SXY rXY = SxSy where sx and sy are the sample standard deviations of X and Y, respectively. (a) Show that the regression R? in the regression of Y on X is the squared value of the sample correlation between X and Y. That is, show that R2 = ry. (b) Show that the R2 from the regression of Y on X is the same as the R2 from the regression of X on Y. (c) Show that Sy = rXY 5. Unbiasedness of OLS estimators (a) Show that beta, can be written as: - iE (X; – X)u; (X; - X)2 (b) Use the result from (a) to show that B1 is an unbiased estimator of B1. (c) Show that Bo is an unbiased estimator of Bo.
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