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Regression Homework Solutions

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

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Regression Homework Solutions

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

  3. EPP 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 EPP 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 EPP 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 EPP 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 EPP 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 <- lm(sqrt(igf1) ~ age, sub=(age>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 EPP 245 Statistical Analysis of Laboratory Data

  9. EPP 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) EPP 245 Statistical Analysis of Laboratory Data

  11. EPP 245 Statistical Analysis of Laboratory Data

  12. EPP 245 Statistical Analysis of Laboratory Data

  13. EPP 245 Statistical Analysis of Laboratory Data

  14. EPP 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 EPP 245 Statistical Analysis of Laboratory Data

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  17. EPP 245 Statistical Analysis of Laboratory Data

  18. EPP 245 Statistical Analysis of Laboratory Data

  19. EPP 245 Statistical Analysis of Laboratory Data

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