Chapter 11--Regression and Correlation Methods

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Unformatted text preview: relation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables An Example Cont’d... x1 4 5 6 7 4 5 6 7 4 5 6 7 Chapter 11: Regression and Correlation Methods x2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 y 4.3 5.5 6.8 8.0 4.0 5.2 6.6 7.5 2.0 4.0 5.7 6.5 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 Bivariate and 3D Scatter Plots 8 8 q q 7 q 7 q q q q q q q q 6 6 10 q q q q q q q y qq 5 5 q 8 q y q q q 6 q q q q x2 y q q 0.5 q 4 q 4 4 q 0.3 2 3 3 0.4 0.2 0.1 0 4.0 q 2 2 q 5.0 6.0 7.0 0.20 x1 Chapter 11: Regression and Correlation Methods 0.30 345678 0.40 x2 Stat 491: Biostatistics x1 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 ANOVA for Multiple Regression Partitioning Sum of Squares, TSS = SSR + SSE . 2 (y − y ) = ¯ (µy |x1 ,x2 ,...,xk − y )2 + ˆ ¯ (y − µy |x1 ,x2 ,...,xk )2 . ˆ Degrees of freedom, n−1 = k + n − (k + 1). That is, dfT = dfR + dfE Mean squares are computed the usual way. SSR SSE MSR = and MSE = . k 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 Standard Error of the Estimate The residuals are deﬁned by, e = y − µy |x1 ,x2 ,··· ,xk . ˆ The residual sum of squares is, (y − µy |...
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