Chapter 11--Regression and Correlation Methods

# xk is the extra regression ss ssrf ssrr sser ssef

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Unformatted text preview: on 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 Tests for Subset of Regression Coeﬃcients Cont’d The contribution of xg +1 , xg +2 , . . . , xk is The extra regression SS = SSRf − SSRr = SSEr − SSEf = The reduction in the error SS This sum of square has, k − g = [n − (g + 1)] − [n − (k + 1)] degrees of freedom. Therefore the above hypothesis can be tested by F= (SSRf − SSRr )/(k − g ) (SSEr − SSEf )/(k − g ) = . SSEf /[n − (k + 1)] SSEf /[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 Tests for Subset of Regression Coeﬃcients Cont’d We reject H0 if F > F1−α,k −g ,n−(k +1) . Separating out the unique (additional) predictive value of xg +1 , xg +2 , . . . , xk is possible if x1 , x2 , . . . , xg are not highly correlated with xg +1 , xg +2 , . . . , xk . That is collinearity causes a problem here as well. The above test can be used to test H0 : βj = 0 vs Ha : βj = 0. How? The above idea can be extended to test a hypothesis like, H0 : βg +1 = βg +2 = · · · = βk vs Ha : at least one of βg +1 , βg +2 , · · · , βk is diﬀerent from the others. How? When does this hypothesis make sense? 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 Subse...
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