ISE 426-526 - Lecture 14 - MLR Part II - B&W

ISE 426-526 - Lecture 14 - MLR Part II - B&W - ISE...

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1 ISE 426-526 Lecture 14 – 2007 Regression Analysis – Part II Model Diagnostics
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2 PRESS Statistic R 2 for Prediction
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3 Lack of Fit • Questions the linear model • Requires repeat observations • Repeat observations are used to obtain an estimate of s 2 • Partitions the residual SS Lack of Fit – cont. 2 ˆ () E ij i SS yy =− y ij = j th observation of the response at x i i = 1,2,…m j = 1, 2, …n 2 11 mn PE ij i ij SS y y == ∑∑ 2 1 ˆ m LOF i i i i SS n y y = If fitted ŷ i is close to the corresponding average ÿ i then there is strong evidence that the regression function is linear. If not it is likely that the regression function is not linear.
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4 Lack of Fit – cont. ANOVA for Lack of Fit
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5 Decision Rule LOF - Example x i y i df 1.3 2.3, 1.8 2.05 2.0 2.8, 1.5 2.15 2.7 2.2 3.3 3.8, 1.8 2.80 3.7 3.7, 1.7 2.70 4.0 2.8, 2.8, 2.2 2.60 4.7 5.4, 3.2, 1.9 3.50 5.0 1.8 5.3 3.5, 2.8, 2.1 2.80 5.7 3.4 6.0 3.2, 3.0 3.10 6.3 3 6.7 5.9
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6 LOF – Example – cont. LOF – Example – ANOVA. The regression equation is yi = 1.44 + 0.338 xi Predictor Coef SE Coef T P Constant 1.4364 0.5900 2.43 0.023 xi 0.3379 0.1319 2.56 0.018 S = 0.981503 R-Sq = 23.0% R-Sq(adj) = 19.5% PRESS = 25.2416
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ISE 426-526 - Lecture 14 - MLR Part II - B&W - ISE...

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