``knitr::opts_chunk\$set(error=TRUE)``

1a Response variable: presence of cancer and cancer recurrence in breast cancer patients with high insulin levels from being overweight

1b Factors: high insulin levels, and obesity

1c Replication could have been used, but not randomization because they are studying a specific disease, breast cancer so it wouldnâ€™t be a completely randomized sample. However, replication was used because the experiment was conducted on a considerable amount of women (512) in the span of 10 years and can be repeated over time.

2a

``boxplot(BMD~g, data=BMDdata, xlab="Treatment", ylab="Bone Mineral Density (BMD)", main="Kudzu Treatments on Bone Mineral Density")``
``## Error in eval(m\$data, parent.frame()): object 'BMDdata' not found``
``mean(treat\$control)``
``## Error in mean(treat\$control): object 'treat' not found``

2b Simple linear regression/One way ANOVA

2c

``lm.BMD <- lm(BMD~g, data=BMDdata)``
``## Error in is.data.frame(data): object 'BMDdata' not found``
``anova(lm.BMD)``
``## Error in anova(lm.BMD): object 'lm.BMD' not found``

2d

``summary(lm.BMD)``
``## Error in summary(lm.BMD): object 'lm.BMD' not found``

Because the p-value 0.00546 is less than Î± =0.05, we reject the null hypothesis. There is significant evidence that the groups differ with respect to mean BMD.

2e

``````control <- c(0.228, 0.207, 0.234, 0.220, 0.217, 0.228, 0.209, 0.221, 0.204, 0.220, 0.203, 0.219, 0.218, 0.245, 0.210)

lowdose <- c(0.211, 0.220, 0.221, 0.233, 0.219, 0.233, 0.226, 0.228, 0.216, 0.225, 0.200, 0.208, 0.198, 0.208, 0.203)

hidose <-  c(0.250, 0.237, 0.217, 0.206, 0.247, 0.228, 0.245, 0.232, 0.267, 0.261, 0.221, 0.219, 0.232, 0.209, 0.255)

t.test(control)``````
``````##
##  One Sample t-test
##
## data:  control
## t = 73.155, df = 14, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  0.2124498 0.2252835
## sample estimates:
## mean of x
## 0.2188667``````

We are 95% confident that the mean BMD for the control treatment group is between 0.2124498 and 0.2252835

``t.test(lowdose)``
``````##
##  One Sample t-test
##
## data:  lowdose
## t = 72.984, df = 14, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  0.2102348 0.2229652
## sample estimates:
## mean of x
##    0.2166``````

We are 95% confident that the mean BMD for the low dose treatment group is between 0.2102348 and 0.2229652.

``t.test(hidose)``
``````##
##  One Sample t-test
##
## data:  hidose
## t = 48.501, df = 14, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  0.2246716 0.2454617
## sample estimates:
## mean of x
## 0.2350667``````

We are 95% confident that the mean BMD for the high dose treatment group is between 0.2246716 and 0.2454617.

2f

``````avg.c <- mean(control)
avg.t <- mean(lowdose+hidose)
treatment.diff <- avg.t-avg.c
treatment.diff``````
``## [1] 0.2328``
``t.test(control, lowdose+hidose, conf.level=0.99)``
``````##
##  Welch Two Sample t-test
##
## data:  control and lowdose + hidose
## t = -36.594, df = 21.358, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 99 percent confidence interval:
##  -0.2507827 -0.2148173
## sample estimates:
## mean of x mean of y
## 0.2188667 0.4516667``````

2g

``````path <- file.path("~","Desktop","CLASSES","PSTAT122","BMDdata.txt")
summary(bmd)``````
``````##       BMD             treat          g
##  Min.   :0.1980   control:15   Min.   :1
##  1st Qu.:0.2100   hidose :15   1st Qu.:1
##  Median :0.2200   lowdose:15   Median :2
##  Mean   :0.2233                Mean   :2
##  3rd Qu.:0.2320                3rd Qu.:3
##  Max.   :0.2670                Max.   :3``````
``````bmdano<-aov(BMD~as.factor(g),data=bmd)
s=split(bmd\$BMD,as.factor(bmd\$g))
summary(bmdano)``````
``````##              Df   Sum Sq   Mean Sq F value Pr(>F)
## as.factor(g)  2 0.003186 0.0015928   7.718 0.0014 **
## Residuals    42 0.008668 0.0002064
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1``````
``````le=tapply(bmd\$BMD,bmd\$g,length)
length(bmd\$BMD);v=length(s);m=3;mse=0.0002064``````
``## [1] 45``
``bd=sum(c(1,-1,0)*tapply(bmd\$BMD,bmd\$g,mean))-qt(0.05/(2*m),n-v,lower.tail=F)*(sqrt(mse*sum(c(1^2,1^2,0^2)*(c(1,1,1)/le))))``
``## Error in qt(0.05/(2 * m), n - v, lower.tail = F): object 'n' not found``
``bu=sum(c(1,-1,0)*tapply(bmd\$BMD,bmd\$g,mean))+qt(0.05/(2*m),n-v,lower.tail=F)*(sqrt(mse*sum(c(1^2))))``
``## Error in qt(0.05/(2 * m), n - v, lower.tail = F): object 'n' not found``
``print(paste('The CI is (',bd,",",bu,')'))``
``## Error in paste("The CI is (", bd, ",", bu, ")"): object 'bd' not found``

2h High dose of Kudzu

2i

``plot(lm.BMD)``
``## Error in plot(lm.BMD): object 'lm.BMD' not found``

Assumptions violated: equal variance Assumptions met: independence, linearity, normality

2j

``use MSE, plug in SSE``
``````## Error: <text>:1:5: unexpected symbol
## 1: use MSE
##         ^``````

3a A set of contrasts Iâ€™d find particularly interesting would be to compare the reaction times of the two treatments, auditory and visual, given the same elapsed time between cue an stimulus. For example, Iâ€™d compare the treatment combinations 1&4, 2&5, and 3&6.

3b

``````path <- file.path("~","Desktop","CLASSES","PSTAT122","reaction.time.txt")
``## Error in eval(predvars, data, env): object 'reaction_time' not found``
``````rxn.lm <- lm(y~Trtmt, data=rxntime)