Regression Least Squares Fitting Equation Formula Latex Code and Summary

Regression Least Squares Fitting

Tags: #math #regression

Equation

$$y_{i}=\alpha + \beta (x_{i} - \bar{x}) + \epsilon_{i} \\ \hat{\alpha}=\bar{y} \\ \hat{\beta}=\frac{s^{2}_{xy}}{s^{2}_{x}}$$

Latex Code

                                 y_{i}=\alpha + \beta (x_{i} - \bar{x}) + \epsilon_{i} \\ \hat{\alpha}=\bar{y} \\ \hat{\beta}=\frac{s^{2}_{xy}}{s^{2}_{x}}

Have Fun

Let's Vote for the Most Difficult Equation!

Introduction

$y_{i}=\alpha + \beta (x_{i} - \bar{x}) + \epsilon_{i} \\ \hat{\alpha}=\bar{y} \\ \hat{\beta}=\frac{s^{2}_{xy}}{s^{2}_{x}}$

To fit a straight line by least squares to n pairs of points (xi,yi), model the observations y by the above equation $y_{i}=\alpha + \beta (x_{i} - \bar{x}) + \epsilon_{i}$ .

Statistics of $s^{2}_{x},s^{2}_{y},s^{2}_{xy}$ is defined as
$s^{2}_{x}=\frac{1}{n}\sum (x_{i}-\bar{x})^{2}$
$s^{2}_{y}=\frac{1}{n}\sum (y_{i}-\bar{y})^{2}$
$s^{2}_{xy}=\frac{1}{n}\sum (x_{i}-\bar{x})(y_{i}-\bar{y})$

Discussion

Comment to Make Wishes Come True

Leave your wishes (e.g. Passing Exams) in the comments and earn as many upvotes as possible to make your wishes come true

Janice Reed

I'm ready to tackle this test head-on.

2023-07-22 00:00
Reply

Timothy Perez reply to Janice Reed

Gooood Luck, Man!

2023-07-30 00:00:00.0
Reply
Anthony Thomas

Wishing for a good outcome on this exam.

2024-01-23 00:00
Reply

Paul Martin reply to Anthony Thomas

Gooood Luck, Man!

2024-02-09 00:00:00.0
Reply
James Williams

It is my deepest desire to pass this exam.

2023-11-25 00:00
Reply

Justin Turner reply to James Williams

Nice~

2023-11-26 00:00:00.0
Reply