Chapter 11--Regression and Correlation Methods

124 1345 32469 mean sq 15562 0149 f 104443 p value

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Unformatted text preview: Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coefficients Prediction (Forecasting) Dummy Variables An Example For the example on weight loss of a compound, the ANOVA output Source Regression Error Total Df 2 9 11 Sum Sq 31.124 1.345 32.469 Mean Sq 15.562 0.149 F 104.443 p-value 0.000 Hence, the data provides strong evidence that there is predictive value in exposure time and humidity for the weight loss of the compound. 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 Inference about Individual Partial Regression Coefficients ˆ The estimated standard error of βj is, ˆˆ SE (βj ) = sε 1 (xij − xj ¯ )2 (1 − 2 Rxj ·x1 ,x2 ,...,xj −1 ,xj +1 ,...,xk ) 2 where Rxj ·x1 ,x2 ,...,xj −1 ,xj +1 ,...,xk is the coefficient of determination when xj is regressed on x1 , x2 , . . . , xj −1 , xj +1 , . . . , xk . The variance inflation factor (VIF) defined by, VIFj = 1 , 2 1 − Rxj ·x1 ,x2 ,...,xj −1 ,xj +1 ,...,xk ˆ is a measure of how much the variance of βj (square of the SE) is increased because of collinearity. 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 Inference about Individual Partial Slopes Cont’d... If VIF = 1, then collinearity is not a problem and if VIF > 10 then collinearity is a serious problem. Notice that βj is the expected change in y associated with a unit change in xj keeping the other x s constant. If there is collinearity then, it is not possible to keep other x s constant. As a result it is difficult to estimate βj which with reasonable probable error. In summary, collinearity poses a big problem in making inference about the regression coefficients. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introductio...
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This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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