sum_w5 - SUMMARY OF WEEK 5 STAT4610 Applied Regression...

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Unformatted text preview: SUMMARY OF WEEK 5 [ STAT4610 Applied Regression Analysis ] 1 FALL 10, DR. NEDRET BILLOR| Auburn University Cont’d on CHAPTER 2 Cont’d on Inferences in Regression Confidence Band for the mean response for a given X (i.e. E(Y|X )): For each X in the predictor, compute lower and upper limits for the CI for the mean response E(Y|X), and put all lower and upper confidence limits on the scatter plot to construct a band. This band enables us to see the region in which the entire regression line lies. It is particularly useful for determining the appropriateness of a fitted regression function. 3) Prediction Interval (PI) for a future response Y (i.e.,Y new ): Prediction intervals indicate likely values for a future value of a response random variable at some specified value of explanatory variable (i.e. X ). a) 99.7% PI for Y new when β , β 1 & σ known: E(Y | X ) ± 3* σ b) PI for Y new when β , β 1 & σ un known ( ) xx 2 new S ) X X ( n 1 1 s ) 2 n ( , 2 / 1 t Y ˆ ) Y ( Y future for Interval Prediction )% 1 ( 100 − + + − α − ± α − c) Prediction Band for Future y response for all X:...
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sum_w5 - SUMMARY OF WEEK 5 STAT4610 Applied Regression...

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