Chapter 11--Regression and Correlation Methods

# Medical researchers conducted a study to relate birth

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Unformatted text preview: f life. Medical researchers conducted a study to relate birth weight (gram/100) and estriol level from urine collected over 24 hours (mg/24 hr) in near-term pregnant women. If level of estriol is a predictor of birth weight, then doctors can measure estriol level and decide whether or not to prolong the pregnancy. The scatter plot of the data is displayed on the next slide. a. Is a straight line a reasonable model? b. Obtain and interpret least square estimates of the parameters. c. What is the estimated expected number birth weight in (grams/100) for a women that had 10 mg/24 hr during pregnancy? 13 mg/24 hr? 20 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 R-code bw<-c(25,25,25,27,27,27,24,30,30,31,30,31,30, 28,32,32,32,32,34, 34,34,35,35,34,35,36,37,38,40,39,43) estriol<-c(7,9,9,12,14,16,16,14,16,16,17, 19,21,24,15,16,17,25,27,15,15,15,16,19,18, 17,18,20,22,25,24) plot(bw~estriol,xlab="Estriol",ylab="Birth Weight", main="Scatter Plot of Birth Weight versus Estriol") (rf<-lm(bw~estriol)) lines(fitted(rf)~estriol) sigma<-sqrt(sum(residuals(rf)^2)/(31-2)) sigma pre<-data.frame(estriol=c(10,13,20)) predict(rf,newdata=pre) 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: Scatter diagram and Least Square Line Scatter Plot of Birth Weight versus Estriol 40 q q q q q 35 Birth Weight q q q q q q q q q 30 q q q q q q q q q q q 25 q q q q 10 15 20 Estriol Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics 25 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Example: Output > rf Call: lm(formula = bw ~ estriol) Coefficients: (Interce...
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