A trigonometric identity is given by: cos^2(x/2)=(tanx+sinx)/2tanx

Shapiro-Wilk normality test

data: y
W = 0.93333, p-value = 7.726e-05

>
> par(mfrow=c(1, 1))
> boxplot(x, y)
> boxplot(x, y,col = 101)
> boxplot(x, y,col = 101,size = n)
Error in boxplot.default(x, y, col = 101, size = n) :
object 'n' not found
> (library(foreign))
[1] "foreign" "stats" "graphics" "grDevices"
[5] "utils" "datasets" "methods" "base"
> (library(shapefiles))
Error in library(shapefiles) : there is no package called ‘shapefiles’
> attach(mydata)
Error in attach(mydata) : object 'mydata' not found
> group1 <- leng[klett == 0.25 & temp == 11]
Error: object 'leng' not found
> group2 <- leng[klett == 1 & temp == 11]
Error: object 'leng' not found
> group3 <- leng[klett == 16 & temp == 11]
Error: object 'leng' not found
> # ....
> boxplot(group1, group2, group3, names=c("0.25/11", "1/11", "16/11"))
Error in boxplot(group1, group2, group3, names = c("0.25/11", "1/11", :
object 'group1' not found
> detach(mydata)
Error in detach(mydata) : invalid 'name' argument
> plot(1:30, qt(0.975, 1:30), type="l",
+ ylab="Student´s t", xlab="d.f.", ylim=c(0,15))
> abline(h=qnorm(0.975), lty="dotted")
>
> hist(log(x), probability=TRUE)
Warning message:
In log(x) : NaNs produced
> xnew <- seq(log(min(x)), log(max(x)), length=100)
Error in seq.default(log(min(x)), log(max(x)), length = 100) :
'from' must be a finite number
In addition: Warning message:
In log(min(x)) : NaNs produced
> lines(xnew, dnorm(xnew, mean=mean(log(x)), sd=sd(log(x))), col="red")
Error in lines(xnew, dnorm(xnew, mean = mean(log(x)), sd = sd(log(x))), :
object 'xnew' not found
> x <- seq(0.01, 4, length=100)
> par(mfrow=c(2, 2))
> plot(x, dgamma(x, .5, .5), type="l")
> plot(x, dgamma(x, .8, .8), type="l")
> plot(x, dgamma(x, 2, 2), type="l")
> plot(x, dgamma(x, 10, 10), type="l")
>
> x1 <- rnorm(100, mean = 50, sd = 10) # normal distribution
> x2 <- runif(100, min = 30, max = 70) # uniform distribution
> x3 <- rlnorm(100, meanlog = 2, sdlog = 1) # lognormal distribution
> boxplot(x1, x2, x3,
+ names=c("Normal", "Uniform", "Lognormal"))
>
> x1 <- c(2, 3, 4, 5, 6)
> x2 <- c(3, 4, 7, 6, 8)
> t.test(x1, x2, var.equal=TRUE) # p=0.20

Two Sample t-test

data: x1 and x2
t = -1.372, df = 8, p-value = 0.2073
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.28924 1.08924
sample estimates:
mean of x mean of y
4.0 5.6