multiple linear regression - important things to know Flashcards
1
Q
state the multiple linear regression formula
A
yᵢ = β₀ + β₁xᵢ₁ + β₂xᵢ₂ + … + βₖxᵢₖ
2
Q
state the multiple linear regression formula in matrix form
A
y = Xβ + ε
3
Q
what is LSE for multiple linear regression in matrix form
A
S(β) = (y-Xβ)ᵀ(y-Xβ)
then after partial derivatives we have
β ̂= (XᵀX)⁻¹Xᵀy
4
Q
what is E(ε)?
(multiple LR, matrix form)
A
zero matrix
5
Q
what is cov(ε)?
(multiple LR, matrix form)
A
σ²𝐈n
6
Q
what is E(y)?
(multiple LR, matrix form)
A
Xβ
7
Q
what is cov(y)?
(multiple LR, matrix form)
A
σ²𝐈n