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

2. 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)

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4. October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 4 > coef(rmr.lm) (Intercept) body.weight 811.226674 7.059528 > 811.226674 + 7.059528*70 [1] 1305.394 > sum(coef(rmr.lm)*c(1,70)) [1] 1305.394 > predict(rmr.lm,data.frame(body.weight=70)) [1] 1305.394

5. 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 -245.74 -113.99 -32.05 104.96 484.81 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 811.2267 76.9755 10.539 2.29e-13 *** body.weight 7.0595 0.9776 7.221 7.03e-09 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 157.9 on 42 degrees of freedom Multiple R-Squared: 0.5539, Adjusted R-squared: 0.5433 F-statistic: 52.15 on 1 and 42 DF, p-value: 7.025e-09

6. October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 6 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 811.2267 76.9755 10.539 2.29e-13 *** body.weight 7.0595 0.9776 7.221 7.03e-09 *** > 7.0595 - 1.96*0.9776 [1] 5.143404 > 7.0595 + 1.96*0.9776 [1] 8.975596 > 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$coef Estimate Std. Error t value Pr(>|t|) (Intercept) 811.226674 76.9755034 10.53876 2.288384e-13 body.weight 7.059528 0.9775978 7.22130 7.025380e-09 > class(tmp$coef) [1] "matrix" > dim(tmp$coef) [1] 2 4

7. October 27, 2004EPP 245 Statistical Analysis of Laboratory Data 7 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 811.2267 76.9755 10.539 2.29e-13 *** body.weight 7.0595 0.9776 7.221 7.03e-09 *** > 7.0595 - 1.96*0.9776 [1] 5.143404 > 7.0595 + 1.96*0.9776 [1] 8.975596 > tmp$coef[2,1] - 1.96*tmp$coef[2,2] [1] 5.143436 > tmp$coef[2,1] + 1.96*tmp$coef[2,2] [1] 8.97562

8. 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 -4.8642 -1.1661 0.1018 0.9450 4.1136 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 18.71025 0.49462 37.828 <2e-16 *** age -0.10533 0.01072 -9.829 <2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 1.741 on 120 degrees of freedom Multiple R-Squared: 0.446, Adjusted R-squared: 0.4414 F-statistic: 96.6 on 1 and 120 DF, p-value: < 2.2e-16

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10. 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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15. 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) 3.83697 0.38021 10.092 <2e-16 *** age 0.10350 0.03954 2.618 0.0103 * --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 1.478 on 98 degrees of freedom Multiple R-Squared: 0.06536, Adjusted R-squared: 0.05582 F-statistic: 6.853 on 1 and 98 DF, p-value: 0.01025 Exercise 5.3

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