Chapter 11--Regression and Correlation Methods

1 2 2 apply log y if x 2 x y 2 apply y if x y x

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Unformatted text preview: decreases (increases) , try y = β0 + β1 x + β2 x 2 + ε. 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 Variance Stabilizing Transformations Suppose the variance increases (decreases) with the predicted value of y . 1 2 2 Apply log y if σε|x ∝ µ2 |x . y √ 2 Apply y if σε|x ∝ µy |x . Suppose the variance increases with the predicted value of y and 1 2 Scatter plot indicates a relationship that increases (decreases) but at a decreasing rate, try y 2 Scatter plot indicates a relationship that increases (decreases) but at a increasing rate , try ln y and also ln x . 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 q q q q 150000 6.5 q q q y pH q q q 5.5 q q 2 3 4 5 6 7 0 q 1 8 q q 0 q q q q q q q qqq q 1 qq 3 4 12 x q qq qq 10 q 6.5 q q q q q 8 pH qq q qq qq q q q q q q q q 6 6.0 q q q qq q qq q q q qq qq q q q qq qq q qq q q qq q q q q q q qqq q q q q q qq q q log(y) 7.0 qq 2 TAS q q q q q 0.5 1.0 1.5 2.0 log(TAS) Chapter 11: Regression and Correlation Methods 4 5.5 q 0.0 q q q qq qq q q qq q qq q q qq q q q qq q q q q q q q q q q q q qq q q qqq q q q qq q 50000 6.0 q q 100000 7.0 Scatter Plot: Two Examples q 0 1 2 3 x Stat 491: Biostatistics 4 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Residual Plots Residuals are defined as e = y − µy |x . which are estimates of ε ˆ and, thus, are used to check for violation of the assumptions. We use studentized residuals and the following plots. 1 Residuals versus the predicted values µy |x : This plot is used to ˆ check for lack of fit and constant variance. The rstudent() and fitted() are us...
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