Chapter 11--Regression and Correlation Methods

There is much more precision in predicting the

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Unformatted text preview: meters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Predicting an Individual Value Cont’d... A 100(1 − α)% prediction interval is given by: yn+1 ± t1−α/2,n−2 SE (ˆn+1 ). ˆ y For the birthweight-estriol example, 95% prediction interval is 1, 937 grams to 3, 584 grams. There is much more precision in predicting the expected birth weight from a population of women than that of an individual woman’s. In R, to construct confidence and prediction intervals: pre<-data.frame(estriol=c(10)) predict(rf,newdata=pre) predict(rf,newdata=pre,interval="confidence",level=0.95 predict(rf,newdata=pre,interval="prediction",level=0.95 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 Simultaneous Intervals Suppose we are interested in simultaneously predicting for more than one value of x (say xn+1 , xn+2 , . . . , xn+m ). We use the cut-off point 2F1−α,2,n−2 instead of t1−α/2,n−2 for our confidence (prediction) intervals to make them simultaneous confidence (prediction) intervals. The resulting intervals are called Working-Hotelling simultaneous confidence (prediction) intervals. 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 Scatter Plots Scatter diagram can display violation of the linearity. Corrective action depends on whether the variance is constant. Suppose variance is constant. Only x is transformed. 1 2 Scatter plot indicates a relationship√ that increases (decreases) but at a decreasing rate, try log x , x or 1/x . Scatter plot indicates a relationship that increases (decreases) but at an increasing rate, try y = β0 + β1 x + β2 x 2 + ε 3 which is a multiple regression. Scatter plot indicates a parabolic relationship, increases (decreases) to a maximum (minimum) then...
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