Homework Help is Here – Start Your Trial Now!
Math
Statistics
4. Suppose b₁ is the least squares estimator of the slope coefficient in a regression of Y on X and b₂ is the slope coefficient estimator in a "reverse" regression of X on Y. Show that R² = b₁ b₂ where R is the correlation between Y and X. b. From a sample of 200 observations the following quantities were calculated: Σx = 11, Σy = 20, Σx2 = 12, Σ xx = 22, Σγ = 84 ΣXY: Estimate both regression equations and calculate R². Calculate the standard error of b₁.

4. Suppose b₁ is the least squares estimator of the slope coefficient in a regression of Y on X and b₂ is the slope coefficient estimator in a "reverse" regression of X on Y. Show that R² = b₁ b₂ where R is the correlation between Y and X. b. From a sample of 200 observations the following quantities were calculated: Σx = 11, Σy = 20, Σx2 = 12, Σ xx = 22, Σγ = 84 ΣXY: Estimate both regression equations and calculate R². Calculate the standard error of b₁.

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

Please help to solve and explain in detail. Thank you! 

### Problem 4 #### a. Suppose \( b_1 \) is the least squares estimator of the slope coefficient in a regression of Y on X and \( b_2 \) is the slope coefficient estimator in a “reverse” regression of X on Y. Show that \( R^2 = b_1 b_2 \) where \( R \) is the correlation between Y and X. #### b. From a sample of 200 observations, the following quantities were calculated: \[ \sum X = 11, \sum Y = 20, \sum X^2 = 12, \sum XY = 22, \sum Y^2 = 84 \] Estimate both regression equations and calculate \( R^2 \). Calculate the standard error of \( b_1 \). (Note: Equations and symbols are provided to give an accurate understanding of the variables and calculation processes required in this problem set.)
Transcribed Image Text:### Problem 4 #### a. Suppose \( b_1 \) is the least squares estimator of the slope coefficient in a regression of Y on X and \( b_2 \) is the slope coefficient estimator in a “reverse” regression of X on Y. Show that \( R^2 = b_1 b_2 \) where \( R \) is the correlation between Y and X. #### b. From a sample of 200 observations, the following quantities were calculated: \[ \sum X = 11, \sum Y = 20, \sum X^2 = 12, \sum XY = 22, \sum Y^2 = 84 \] Estimate both regression equations and calculate \( R^2 \). Calculate the standard error of \( b_1 \). (Note: Equations and symbols are provided to give an accurate understanding of the variables and calculation processes required in this problem set.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 19 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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