DataM: Inclass Exercise 0413

In-class exercise 1.

Run the following R script to see what happens. Change the ‘df’ parameter to a slightly larger integer and do it again. What statistical concept does this script illustrate?

x <- seq(-pi*2, 2*pi, .05)
z <- dnorm(x)
y <- dt(x, df=3)
plot(x, z, type="l", bty="L", xlab="Standard unit", ylab="Density")
polygon(c(x, rev(x)), c(y, rev(z)), col='aliceblue')
lines(x, y, col='cadetblue')

[Solution and Answer]

Put plotting codes into a function to avoid massive replicated codes.

f_plot <- function(df) {
  x <- seq(-pi*2, 2*pi, .05)
  z <- dnorm(x)
  y <- dt(x, df=df)
  plot(x, z, type="l", bty="L", xlab="Standard unit", ylab="Density")
  polygon(c(x, rev(x)), c(y, rev(z)), col='aliceblue')
  lines(x, y, col='cadetblue')
  text(-4, 0.3, paste0('df = ', df))    # add this command to show df value for each plots
}

Use different values of df to call f_plot to find the change.

for (df in c(3, 5, 8, 12, 17, 23, 30)) {
  f_plot(df=df)
}

From these plots, we can know that these codes try to illustrate that the t distribution gets closer to the standard normal distribution as the degree of freedom increases.

In-class exercise 2.

Doll (1955) showed per capita consumption of cigarettes in 11 countries in 1930, and the death rates from lung cancer for men in 1950. Use R base graphics to generate the plot shown below.
Source: Freedman, et al. (1997). Statistics. pp. 148-150.

[Solution and Answer]

dta2 <- read.table('../data/inclass0413_2.txt', header=TRUE)
head(dta2)

str(dta2)

'data.frame':   11 obs. of  3 variables:
 $ Country    : Factor w/ 11 levels "Australia","Canada",..: 1 2 3 4 10 5 6 7 8 9 ...
 $ consumption: int  480 500 380 1100 1100 230 490 250 300 510 ...
 $ death      : int  180 150 170 350 460 60 240 90 110 250 ...

plot(dta2$consumption, dta2$death, xlab = 'Death rate (per million)', ylab = 'Consumption (per captia per year)',
     main = 'Lung Cancer and Cigratte Consumption', col='white')
text(dta2$consumption, dta2$death, dta2$Country)
abline(lm(death ~ consumption, data = dta2), lty=2)

In-class exercise 3.

Use R base graphics to create the national flag of Denmark.

Target output

[Solution and Answer]

op <- par(bg='red')
plot.new()
par(mar = c(0, 0, 0, 0))  # close the inner margins
par(oma = c(0, 0, 0, 0))  # close the outer margins
plot.window(xlim=c(0, 37), ylim=c(0, 28))
abline(h=14, col='white', lwd=96*4) # since one unit in lwd equal 1/96 inch
abline(v=14, col='white', lwd=96*4)

par(op)

In-class exercise 4.

Run the R script to see what happens first and then explain how the effect is achieved by the script.

[Solution and Answer]

n <- 60
t <- seq(0, 2*pi, length=n)
x <- sin(t)
y <- cos(t)
#
par(pty = "s")
#
for (i in 1:n) {
  plot.new()
  plot.window(c(-1, 1), c(-1, 1))
  lines(x*y, -y, col="gray")
  points(x[i]*y[i], -y[i], pch=16,
  col=gray((i-1)/(n+1)))
  Sys.sleep(.05)
}

This script drew n (e.g., 60 here) plots to demonstrate a point roll along with a 8-shape curve. The color of the point get lighter when rolling.

In-class exercise 5.

Draw a pie chart to represent 50 shades of gray. Hint: Use ?gray to examine the gray level specification documented for the gray{grDevices}. Use ?pie to study the function for making pie charts documented for pie{graphics}.

[Solution and Answer]

par(mar = c(0, 0, 0, 0))  # close the inner margins
par(oma = c(0, 0, 0, 0))  # close the outer margins
pie(table(1:50), col = gray(seq(0, 1, by=1/50)))