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

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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 ...
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