Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ (Υ - Y)2 Σ1(Yi-Y)²¹ SXY √SXX SYY where Sxy=₁1 (X₁ — X)(Y; — Y), Sxx = Σ₁-1 (X₁ — X)², Syy = ₁₁(Y₁ - Y)². R²: = TXY =
Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ (Υ - Y)2 Σ1(Yi-Y)²¹ SXY √SXX SYY where Sxy=₁1 (X₁ — X)(Y; — Y), Sxx = Σ₁-1 (X₁ — X)², Syy = ₁₁(Y₁ - Y)². R²: = TXY =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Question 2. Show that, for a simple linear regression, R² = ry, where R² is the
coefficient of determination and rxy is the sample correlation between Y and X.
Hint:
Σ" (Υ - Y)2
Σ1(Y₁-Y)²¹
SxY
√SXXSYY'
where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)².
R²
=
"XY =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2Fd3050a4b-6be2-444f-8d2b-1329a3ceef8c%2Fmlx5htc_processed.png&w=3840&q=75)
Transcribed Image Text:Question 2. Show that, for a simple linear regression, R² = ry, where R² is the
coefficient of determination and rxy is the sample correlation between Y and X.
Hint:
Σ" (Υ - Y)2
Σ1(Y₁-Y)²¹
SxY
√SXXSYY'
where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)².
R²
=
"XY =
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