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X & Y are random variables Follow a joint probability distribution.    Have finite 1st & 2nd...

X & Y are random variables

  • Follow a joint probability distribution.   
  • Have finite 1st & 2nd moments.
  • Var(X)≠0.

Real numbers a & b, which minimize E[(Y – a − bX)^2] over all possible (a,b) are being determined for least squares/theoretical linear regression of Y on X.

Solve f(a,b) = E[(Y – a − bX)^2] in order to find the critical points where the gradient equals 0.

Differentiation & expectation can be switched with respect to a & b, such that ∂aE[(⋯)] = E[∂a(⋯)]

  1. Partial derivative: ∂af = E[ ___________ ]
  2. Partial derivative: ∂bf = E[ ___________ ]
Math   Statistics-And-Probability   
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