1 Regression Homework Solutions EPP 245/298 Statistical Analysis of Laboratory Data.

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1 Regression Homework Solutions EPP 245/298 Statistical Analysis of Laboratory Data

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 2 Exercise 5.1 > library(ISwR) > data(rmr) > attach(rmr) > names(rmr) [1] "body.weight" "metabolic.rate" > plot(body.weight,metabolic.rate) > rmr.lm <- lm(metabolic.rate ~ body.weight) > abline(coef(rmr.lm),col="red",lwd=2)

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 3

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 4 > coef(rmr.lm) (Intercept) body.weight > *70 [1] > sum(coef(rmr.lm)*c(1,70)) [1] > predict(rmr.lm,data.frame(body.weight=70)) [1]

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 5 > summary(rmr.lm) Call: lm(formula = metabolic.rate ~ body.weight) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) e-13 *** body.weight e-09 *** --- Signif. codes: 0 `***' `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: on 42 degrees of freedom Multiple R-Squared: , Adjusted R-squared: F-statistic: on 1 and 42 DF, p-value: 7.025e-09

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 6 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) e-13 *** body.weight e-09 *** > * [1] > * [1] > tmp <- summary(rmr.lm) > names(tmp) [1] "call" "terms" "residuals" "coefficients" [5] "aliased" "sigma" "df" "r.squared" [9] "adj.r.squared" "fstatistic" "cov.unscaled" > tmp$coef Estimate Std. Error t value Pr(>|t|) (Intercept) e-13 body.weight e-09 > class(tmp$coef) [1] "matrix" > dim(tmp$coef) [1] 2 4

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 7 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) e-13 *** body.weight e-09 *** > * [1] > * [1] > tmp$coef[2,1] *tmp$coef[2,2] [1] > tmp$coef[2,1] *tmp$coef[2,2] [1]

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 8 Exercise 5.2 > data(juul) > names(juul) [1] "age" "menarche" "sex" "igf1" "tanner" "testvol" > attach(juul) > juul.lm 25)) > summary(juul.lm) Call: lm(formula = sqrt(igf1) ~ age, subset = (age > 25)) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) <2e-16 *** age <2e-16 *** --- Signif. codes: 0 `***' `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: on 120 degrees of freedom Multiple R-Squared: 0.446, Adjusted R-squared: F-statistic: 96.6 on 1 and 120 DF, p-value: < 2.2e-16

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 9

October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 10 > plot(age,igf1) > plot(age[age>25],igf1[age>25]) > abline(coef(lm(igf1 ~ age,sub=(age>25))),col="red",lwd=2) > plot(age[age>25],sqrt(igf1)[age>25]) > abline(coef(juul.lm),col="red",lwd=2)

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October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 15 > data(malaria)> > names(malaria) [1] "subject" "age" "ab" "mal" > attach(malaria) > hist(ab) > hist(log(ab)) > plot(age,log(ab)) > summary(lm(log(ab) ~ age)) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) <2e-16 *** age * --- Signif. codes: 0 `***' `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: on 98 degrees of freedom Multiple R-Squared: , Adjusted R-squared: F-statistic: on 1 and 98 DF, p-value: Exercise 5.3

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October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 19