Chapter 11--Regression and Correlation Methods

Csvhersdatacsvheadert nondiabetic

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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 Confounding: R-codes for the example Diabetes<-read.csv("hersdata.csv",header=T) NonDiabetic<-Diabetes[Diabetes$glucose<=125,] dmlr<-lm(glucose~exercise+age+drinkany+BMI, data=NonDiabetic) summary(dmlr) library(HH) #The package HH must be installed first vif(dmlr) 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 Multicollinearity (Collinearity) Multicollinearity: is present when the independent variables are correlated themselves. In multiple regression, we are trying to separate the predictive value of each of the independent variables. In the total absence of multicollinearity, which is very unlikely, 2 2 2 2 Ry ·x1 ,x2 ,...,xk = ryx1 + ryx2 + · · · + ryxk . That is, we can precisely separate out the predictive value of each of the x s. In the presence of high multicollinearity, it is difficult to separate the predictive value of the independent variables. 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 Testing for any predictive value in x1 , x2 , . . . , xk The hypotheses, H0 : β 1 = β 2 = . . . = β k = 0 Ha : at least one βi is different from zero. The above H0 is interpreted as there is no predictive value in all of the x s. Test statistic, 2 Ry ·x1 ,x2 ,...,xk /k MSR F= = 2 MSE (1 − Ry ·x1 ,x2 ,...,xk )/[n − (k + 1)] We reject H0 if F ≥ Fα,k ,n−(k +1) . Rejection of H0 tells us evidence of predictive value somewhere in the x s but does Stat 491: Biostatistics which x s. not tell us in Chapter 11: Regression and Correlation Methods Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple...
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