what is the simple linear regression equation

There are four assumptions associated with a linear regression model: Introduction to Statistical Learning (Springer 2013) Instead of the 'line of best fit,' there is a ' plane of best fit.' Here is an example of a linear regression with two predictors and one outcome: The residuals are the fitted values minus the actual observed values of Y. The fitted values (i.e., the predicted values) are defined as those values of Y that are generated if we plug our X values into our fitted model. When we have more than one predictor, we call it multiple linear regression: The betas are chose such that they minimize this expression:Īn instructive graphic I found on the Internet

The betas are selected by choosing the line that minimizing the squared distance between each Y value and the line of best fit. That is, the expected value of Y is a straight-line function of X. When we have one predictor, we call this 'simple' linear regression:

Regression analysis is commonly used for modeling the relationship between a single dependent variable Y and one or more predictors.

What is the simple linear regression equation