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Extending Linear Regression: Weighted Least Squares ...

Extending Linear Regression: Weighted LeastSquares, Heteroskedasticity, Local PolynomialRegression36-350, Data Mining23 October 2009 Contents1 Weighted Least Squares12 Weighted Least Squares as a Solution to Heteroskedasticity ..53 Local Linear Regression104 Exercises151 Weighted Least SquaresInstead of minimizing the residual sum of Squares ,RSS( ) =n i=1(yi ~xi )2(1)we could minimize theweightedsum of Squares ,WSS( , ~w) =n i=1wi(yi ~xi )2(2)This includes ordinary Least Squares as the special case where all the weightswi= 1. We can solve it by the same kind of algebra we used to solve theordinary Linear Least Squares problem. But why would we want to solve it?

The standard errors from the simulation are 0:22 for the intercept and 0:23 for the slope, so R’s internal calculations are working very well. All of this was possible because the Oracle told us what the variance function

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