prediction_variance

prediction_variance -...

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4.2.1 Interpolation, extrapolation and prediction variance Interpolation is mathematically contrasted to regression or least squares fit As important is the contrast between interpolation and extrapolation Extrapolation occurs when we are outside the convex ull of the data points hull of the data points 11 ,1 , 0 , nn ii i i    xx For high dimensional spaces we must have extrapolation!
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rediction variance Prediction variance near regression model ˆ ) , n b Linear regression model efine en 1 () ii i yb x ) m ˆ mT b Define then ith some algebra , x x , y xb With some algebra  1 2 () ˆ [() ] , m T m b Var y X X  xx x x x Standard error 1 ˆ T m y sX X
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Example 4.2.1 For a linear polynomial RS y=b 1 +b 2 x 1 +b 2 x 2 find the prediction variance in the region (a) For data at three vertices (omitting (1,1)) 1 1 , 1 1 2 1 x x       12 3 1, 1 , 1,1 , 1 TT T xx x
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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prediction_variance -...

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