multiple linear regression - important things to know

Question 1

state the multiple linear regression formula

Answer 1

yᵢ = β₀ + β₁xᵢ₁ + β₂xᵢ₂ + … + βₖxᵢₖ

Question 2

state the multiple linear regression formula in matrix form

Answer 2

y = Xβ + ε

Question 3

what is LSE for multiple linear regression in matrix form

Answer 3

S(β) = (y-Xβ)ᵀ(y-Xβ)

then after partial derivatives we have
β ̂= (XᵀX)⁻¹Xᵀy

Question 4

what is E(ε)?
(multiple LR, matrix form)

Answer 4

zero matrix

Question 5

what is cov(ε)?
(multiple LR, matrix form)

Answer 5

σ²𝐈n

Question 6

what is E(y)?
(multiple LR, matrix form)

Answer 6

Xβ

Question 7

what is cov(y)?
(multiple LR, matrix form)

Answer 7

σ²𝐈n