Linear regression: introduction through modeling

Linear regression: introduction through modeling

Consider a simple linear regression (SLR) model:

y: the dependent variable

x: independent variable, or explanatory variable

β0: intercept

β1: slope

ε: deviation or residual,  

Here, the values of x and y are observed and could be measured. Each point (x,y) supposed to be independent. β0 andβ1 are unknown, and should be estimated by a certain method. We assumed that ε is unobserved as independent and identically distributed random variable. So linear regression is a process to estimate unknown parametersβ0, β1, and σ2 using the pairs of values of the variables x and y.

Therefore,

E(

Var(y|x)=σ2

Set