# sum_w4 - SUMMARY OF WEEK 4[STAT4610 Applied Regression...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SUMMARY OF WEEK 4 [STAT4610 Applied Regression Analysis] Cont’d on CHAPTER 2 Cont’d on Inferences in Regression 1) Power of test: The power of this test is the probability that the decision rule will lead to conclusion H1 when H1 in fact holds. Power of test = 1 ‐ Type II Error = P(|to| > t (1 − α/2; n − 2)| δ ) β − β * where , δ = 1 1 , noncentrality parameter : This is a measure of how far the ˆ σ(β1 ) true value of β1 is from β1* ) Table B.5 contains the power of tests concerning the regression parameters (two sided t‐test) for various degrees of freedoms. 2) CI for the mean response for a given X0 (i.e. E(Y|X0)): Sampling Distribution for the point estimator of E(Y given X0) ˆ ˆ (that is: E(Y X 0 )(= Y0 ) ) For normal error regression model: ˆ ⎛ 1 (X − X) 2 ⎞ Y − Y0 ˆ ˆ ⎟ then 0 ~ N(0,1) E(Y0 ) = Y0 , var(Y0 ) = σ 2 ⎜ + 0 ⎜n ˆ S xx ⎟ sd(Y0 ) ⎝ ⎠ Since σ 2 is unknown, use the estimated variance, that is, s 2 then t = ˆ Y0 − Y0 ~ t with n ‐ 2 df ˆ se(Y0 ) 1 (X 0 − X) 2 + n S xx E(Y|X) ˆ where se[Y0 ] = s Then 100(1‐α) percent CI for the mean response (i.e regression line) for a specific X0: 1 (X − X)2 ˆ Y0 ± t(1 − α / 2,(n − 2)) * s + 0 n S xx 1 FALL 10, DR. NEDRET BILLOR| Auburn University ...
View Full Document

## This note was uploaded on 10/12/2010 for the course STAT 4630 taught by Professor Billor during the Spring '10 term at Auburn University.

Ask a homework question - tutors are online