MATH 226 - 10.3.2007

MATH 226 - 10.3.2007 - various variables and their levels...

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MATH 226 – October 3, 2007 Regression – object to build a model, such that observations y can be predicted from x (x 1 , x n ) Comparison of effects o (1) ŷ= α 1 + β 1 xif β 1 > β 2 x has bigger influence on y (2) ŷ= α 2 + β 2 x in model 1 than in 2 o All variables are qualitative Measures of Accuracy o Should be known o R 2 = (Σ(y i – y-bar) 2 - Σ(y i – ŷ i ) 2 )/ Σ(y i – y-bar) 2 o Coefficient of Determination 0 ≤ R 2 ≤ 1 o r correlation coefficient only tells about linear relation between two variables o Residual Plots There should be no pattern Vs. ŷ (fitted value) vs. y vs. x 1 :x n Fitted effects for factorial experiments: some or all of the x’s are qualitative The objective is not to predict, rather to explain the influences of
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Unformatted text preview: various variables and their levels to the response o The variables x 1 :x n are called factors and their values are levels Fitted main effects are defined as the overall difference of a level of the factor as compared to the average o A, B, C are the factors o So the fitted main effect at level i of factor A is a i = y i• bar - y •• bar Fitted interaction effects One goal is to fit the simplest model o μ + α i + β j + αβ ij μ + α i μ + β j Measure of Fit o R 2 o Residuals (y – ŷ) o Absolute value size comparison of effects...
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This note was uploaded on 04/07/2008 for the course MATH 226 taught by Professor Daepp during the Fall '07 term at Bucknell.

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