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Unformatted text preview: STAT 201 Handout 7 Final Words on Regression Prediction vs. Estimation Recall that although the prediction value equals the estimated sub-population mean (i.e. b y x = b Y | x ), prediction error is bigger than estimation error (i.e. SE( b y x ) > SE( b Y | x )). Remember that prediction is a two-tier procedure: 1. guess y x by sub-population mean Y | x 2. estimate unknown Y | x by b Y | x = b + b 1 x Each step above has its own error. The formulas are: SE( b Y | x ) = SE(fit) = s s 1 n + ( x- x ) 2 ( n- 1) s 2 x SE( b y x ) = SE(predicted) = q s 2 + Var( b Y | x ) s = r SSE n- 2 Recall that s is the pooled estimate of the common among all sub-populations, and SSE is the sum of (vertical deviation) 2 . Most of the above values can be picked from a standard regression analysis output. For an example, see text Figure 14.6. Vertical Deviations In regression terminology, these are called residuals ....
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This note was uploaded on 01/23/2012 for the course STAT 201 taught by Professor Staff during the Fall '03 term at Simon Fraser.
- Fall '03