Chapter 11--Regression and Correlation Methods

5234 06082 sigma sqrtsumresidualsrf231 2 sigma 1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: pt) estriol 21.5234 0.6082 > sigma<-sqrt(sum(residuals(rf)^2)/(31-2)) > sigma [1] 3.82111 > pre<-data.frame(estriol=c(10,13,20)) > predict(rf,newdata=pre) 1 2 3 27.60533 29.42990 33.68724 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 Example Cont’d ... b. Interpreting parameter estimates: ˆ From β1 = 0.6082, we conclude that for a 1mg/24 hr increase in the estriol level, there is an estimated expected increase of 60.82 grams in birth weight. ˆ Interpreting β0 would be extrapolation. The standard deviation around the line (the residual standard deviation) of sε = 3.8211 indicates that about 95% of the prediction errors should be between ±2(3.8211) = ±7.6422. c. Since, = 21.5234 + 0.6082(10) = 27.605 we expect the birth weight would be 2.76kg for a women who had estriol level of 10 mg/24 hr. 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 ˆ ˆ Standard Errors of β0 and β1 Standard Error of an estimate indicates how accurately one can estimate the correct population value. ˆ ˆ The standard errors of β1 and β0 denoted, respectively, by σβ1 ˆ and σβ1 are given by ˆ σε σβ1 = √ ˆ Sxx and σβ0 = σε ˆ 1 x2 ¯ + . n Sxx ˆ Therefore, the quality of estimation of β1 is influenced by the 2 and the amount of variation in the error variance σε independent variable Sxx . The ideal situation for estimating β0 is when x = 0. Why? ¯ 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 Inference about β1 The hypothesis x...
View Full Document

Ask a homework question - tutors are online