Homework Help is Here – Start Your Trial Now!
Math
Statistics
SXY rXY = sx and sy are the sample standard deviations of X and Y, respec Show that the regression R2 in the regression of Y on X is the correlation between X and Y. That is, show that R² = r?y. Show that the R² from the regression of Y on X is the same as the on Y. Show that SY B1 = rxY SX

SXY rXY = sx and sy are the sample standard deviations of X and Y, respec Show that the regression R2 in the regression of Y on X is the correlation between X and Y. That is, show that R² = r?y. Show that the R² from the regression of Y on X is the same as the on Y. Show that SY B1 = rxY SX

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
See similar textbooks
icon
Related questions
Question
4. The sample covariance of two random variables X and Y in a sample of size n is given by n 1 SXY = (X; - X)(Y; – Ỹ). п — 1 i=1 The sample correlation is then given by SXY rXY = sx sY 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 R? = 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 Bi = Sy = rXY SX
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 = (X; - X)(Y; – Ỹ). п — 1 i=1 The sample correlation is then given by SXY rXY = sx sY 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 R? = 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 Bi = Sy = rXY SX
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS