Homework9_2
Kunal Dolas
12/5/2020
The anaesthetic data provides the time to restart breathing unassisted in recovering from general anaesthetic for four treatment groups. Produce a boxplot depicting the data. Comment on any features of interest.
library(faraway)
data(anaesthetic)
anaesthetic## breath tgrp
## 1 3 A
## 2 6 B
## 3 3 C
## 4 4 D
## 5 2 A
## 6 4 B
## 7 5 C
## 8 8 D
## 9 1 A
## 10 1 B
## 11 2 C
## 12 2 D
## 13 4 A
## 14 1 B
## 15 4 C
## 16 3 D
## 17 3 A
## 18 6 B
## 19 2 C
## 20 2 D
## 21 2 A
## 22 2 B
## 23 1 C
## 24 3 D
## 25 10 A
## 26 1 B
## 27 6 C
## 28 6 D
## 29 12 A
## 30 10 B
## 31 13 C
## 32 2 D
## 33 12 A
## 34 1 B
## 35 1 C
## 36 3 D
## 37 3 A
## 38 1 B
## 39 1 C
## 40 4 D
## 41 19 A
## 42 1 B
## 43 1 C
## 44 8 D
## 45 1 A
## 46 2 B
## 47 4 C
## 48 5 D
## 49 4 A
## 50 10 B
## 51 1 C
## 52 10 D
## 53 5 A
## 54 2 B
## 55 1 C
## 56 2 D
## 57 1 A
## 58 2 B
## 59 1 C
## 60 0 D
## 61 1 A
## 62 2 B
## 63 8 C
## 64 10 D
## 65 7 A
## 66 2 B
## 67 1 C
## 68 2 D
## 69 5 A
## 70 1 B
## 71 2 C
## 72 3 D
## 73 1 A
## 74 3 B
## 75 4 C
## 76 9 D
## 77 12 A
## 78 7 B
## 79 0 C
## 80 1 Dplot(breath ~ tgrp, data=anaesthetic,ylab="Time (min)")
stripchart(breath ~ tgrp, data=anaesthetic, vertical=TRUE, method="stack",
xlab="Group Subject to Treatment",ylab="Time (min)")
For group B, the median and lower tertile.
Fit a one-factor model for the recovery times. Which pairs of treatments are different?
lmod<-lm(breath ~ tgrp,anaesthetic)
sumary(lmod)## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.40000 0.81598 6.6178 4.567e-09
## tgrpB -2.15000 1.15397 -1.8631 0.06631
## tgrpC -2.35000 1.15397 -2.0364 0.04519
## tgrpD -1.05000 1.15397 -0.9099 0.36575
##
## n = 80, p = 4, Residual SE = 3.64917, R-Squared = 0.07round(coef(lmod),1)## (Intercept) tgrpB tgrpC tgrpD
## 5.4 -2.2 -2.4 -1.1model.matrix(lmod)## (Intercept) tgrpB tgrpC tgrpD
## 1 1 0 0 0
## 2 1 1 0 0
## 3 1 0 1 0
## 4 1 0 0 1
## 5 1 0 0 0
## 6 1 1 0 0
## 7 1 0 1 0
## 8 1 0 0 1
## 9 1 0 0 0
## 10 1 1 0 0
## 11 1 0 1 0
## 12 1 0 0 1
## 13 1 0 0 0
## 14 1 1 0 0
## 15 1 0 1 0
## 16 1 0 0 1
## 17 1 0 0 0
## 18 1 1 0 0
## 19 1 0 1 0
## 20 1 0 0 1
## 21 1 0 0 0
## 22 1 1 0 0
## 23 1 0 1 0
## 24 1 0 0 1
## 25 1 0 0 0
## 26 1 1 0 0
## 27 1 0 1 0
## 28 1 0 0 1
## 29 1 0 0 0
## 30 1 1 0 0
## 31 1 0 1 0
## 32 1 0 0 1
## 33 1 0 0 0
## 34 1 1 0 0
## 35 1 0 1 0
## 36 1 0 0 1
## 37 1 0 0 0
## 38 1 1 0 0
## 39 1 0 1 0
## 40 1 0 0 1
## 41 1 0 0 0
## 42 1 1 0 0
## 43 1 0 1 0
## 44 1 0 0 1
## 45 1 0 0 0
## 46 1 1 0 0
## 47 1 0 1 0
## 48 1 0 0 1
## 49 1 0 0 0
## 50 1 1 0 0
## 51 1 0 1 0
## 52 1 0 0 1
## 53 1 0 0 0
## 54 1 1 0 0
## 55 1 0 1 0
## 56 1 0 0 1
## 57 1 0 0 0
## 58 1 1 0 0
## 59 1 0 1 0
## 60 1 0 0 1
## 61 1 0 0 0
## 62 1 1 0 0
## 63 1 0 1 0
## 64 1 0 0 1
## 65 1 0 0 0
## 66 1 1 0 0
## 67 1 0 1 0
## 68 1 0 0 1
## 69 1 0 0 0
## 70 1 1 0 0
## 71 1 0 1 0
## 72 1 0 0 1
## 73 1 0 0 0
## 74 1 1 0 0
## 75 1 0 1 0
## 76 1 0 0 1
## 77 1 0 0 0
## 78 1 1 0 0
## 79 1 0 1 0
## 80 1 0 0 1
## attr(,"assign")
## [1] 0 1 1 1
## attr(,"contrasts")
## attr(,"contrasts")$tgrp
## [1] "contr.treatment"anova(lmod)## Analysis of Variance Table
##
## Response: breath
## Df Sum Sq Mean Sq F value Pr(>F)
## tgrp 3 70.94 23.646 1.7757 0.1589
## Residuals 76 1012.05 13.316no treatments are really different.
Try the Box-Cox transformation method. Explain what went wrong.
require(MASS)## Loading required package: MASSlibrary(faraway)
data(anaesthetic)
#lmod<-lm(breath ~ tgrp,anaesthetic)
#boxcox(lmod,plotit=T)It did not run successfully as the response variable is not positive.
Try a square root transformation on the response. Are the diagnostics satisfactory? Is there a significant difference among treatment groups?
plot(fitted(lmod),residuals(lmod),xlab="Fitted",ylab="Residuals")
abline(h=0)
plot(fitted(lmod),sqrt(abs(residuals(lmod))), xlab="Fitted",ylab=
expression(sqrt(hat(epsilon))))
sumary(lm(sqrt(abs(residuals(lmod))) ~ fitted(lmod)))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.82561 0.28636 2.8831 0.005087
## fitted(lmod) 0.18188 0.06948 2.6177 0.010628
##
## n = 80, p = 2, Residual SE = 0.58519, R-Squared = 0.08There is no significant difference between the treatments.