An Introduction to Simple Linear Regression
•The model:
yi=β0+β1xi+i, i =...,n (1)
β0is the intercept parameter; β1the slope parameter.
•is a random variable (random error) with
E() = 0) and V ar(E) = σ2
•This implies yis a random variable with
mean E(y) = β0+β1xand variance σ2
•For statistical inference. it is also assumed that the
’s are a random sample from the normal distribution.
•This implies that y-values observed at each x-value
are a random sample from a normal distribution with
the mean E(y) = µ(x) = β0+β1xand variance σ2.
•Esimation: Minimize
X
i(yi−ˆyi)2=X
i(yi−ˆ
β0−ˆ
β1xi)2
to obtain least squares estimates ˆ
β0and ˆ
β1
•Regression Anova table:
Source df Sum of Mean F
Squares Square
Regression 1 SSReg MSReg=SSReg/1 MSReg/MSE
Error n−2 SSE MSE=SSE/(n−2)
Total n−1 SSTot
