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Chapter 11--Regression and Correlation Methods

# Example interpret the parameter estimates for the

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Unformatted text preview: the interpretation of the partial regression coeﬃcients changes. For additive models, βj is interpreted as the expected change in y for a unit change in xj when all other x s are held constant. Example: Interpret the parameter estimates for the productivity example above. This does not hold for the nonadditive models. In general there is no literal interpretation of the partial slopes. The focus is on ﬁnding a multiple regression that provides a good ﬁt for the data, not on interpreting individual β s. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables Least Square Estimation ˆˆ ˆ The values (β0 , β1 . . . , βk ) which minimize f (β0 , β1 . . . , βk ) = [y − (β0 + β1 x1 + · · · + βk xk )]2 . 2 The least square estimate of σε is 2 sε = (y − µy |x1 ,...,xk )2 ˆ . n − (k + 1) Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables Least Square Estimation: Example Example: Twelve observations were collected on the weight loss of a compounds (pounds) y , the amount of time the compound was exposed to the air (hours) x1 and the humidity of the environment during exposure x2 . In R, summary(lm(y~x1+x2)) ˆ ˆ The least square estimates are β0 = 0.667, β1 = 1.317, ˆ2 = −8.000 and sε = 0.3872 = 0.150. β Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Cor...
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