multiple linear regression - important things to know Flashcards

1
Q

state the multiple linear regression formula

A

yᵢ = β₀ + β₁xᵢ₁ + β₂xᵢ₂ + … + βₖxᵢₖ

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2
Q

state the multiple linear regression formula in matrix form

A

y = Xβ + ε

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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

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4
Q

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

A

zero matrix

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5
Q

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

A

σ²𝐈n

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6
Q

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

A

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7
Q

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

A

σ²𝐈n

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