How do I prove that it does pass through (mean x, mean y) 2.89 A property of the least-squares regressionline. Use the equation for the least-squares regressionline to show that this line always passes through thepoint (x, y).

Name: How do I prove that it does pass through (mean x, mean y) 2.89 A prope
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Description: How do I prove that it does pass through (mean x, mean y) 2.89 A property of the least-squares regressionline. Use the equation for the least-squares regressionline to show that this line always passes through thepoint (x, y).

Answered: 2.89 A property of the least-squares…

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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How do I prove that it does pass through (mean x, mean y)

2.89 A property of the least-squares regression
line. Use the equation for the least-squares regression
line to show that this line always passes through the
point (x, y).

Expert Solution

Step 1

Suppose we are given a straight line

y=a+bx

, then we say that the line passes through the point (x₀, y₀ ), if and only if:

a+bx₀ = y₀ is satisfied.

In our case, we need to show that the line of regression always passes through ( $x, y$ ),

First recall the equation of least squares is given by:

y- $y$ = $\frac{c o v (x, y)}{{σ_{x}}^{2}}$ (x- $x$ ), where cov(x,y) is the covariance between X and Y, and ${σ_{x}}^{2}$ is the variance of X

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