C Other useful R functions

C.1 General functions

seq() produces a sequence of integers:
- seq(1, 4) produces the list: \(1\), \(2\), \(3\), \(4\).
- seq(0, 10, by = 2) produces a list going up by two each time: \(0\), \(2\), \(4\), \(6\), \(8\), \(10\).
- seq(0, 10, length = 3) produces a list of length three: \(0\), \(5\), \(10\).
- A colon can also be used in special cases: 3 : 7 produces: \(3\), \(4\), \(5\), \(6\), \(7\).
c() is used to concatenate (join together) a series of values:
- c("fred", "martha") creates a vector with two text elements.
- c(1, 8, 3.14, -2)create a vector with four numerical elements.
cat() is often used to print information.
array( dim = c(2, 4)) produces an empty \(2\times 3\) array (which is like a matrix).
array( data = c(1, 2, 3, 4, 5, 6), dim = c(2, 3)) produces the \(2\times 3\) array \[ \left[ \begin{array}{ccc} 1 & 3 & 5\\ 2 & 4 & 6\\ \end{array} \right]. \]
array( data = c(1, 2, 3, 4, 5, 6), byrow = TRUE, dim = c(2, 3)) produces the \(2\times 3\) array \[ \left[ \begin{array}{ccc} 1 & 2 & 3\\ 4 & 5 & 6\\ \end{array} \right]. \]
t() transposes a matrix or array.

Logical comparison in R are possible (notice the use of ==):

DaysOfWeek <- c("Mon", "Tues", "Wed", "Thurs", "Fri", "Sat", "Sun")
HoursSleep <- c(8, 8, 8, 8, 6, 6, 10)

HoursSleep == 8
#> [1]  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE
HoursSleep > 8
#> [1] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
HoursSleep >= 8
#> [1]  TRUE  TRUE  TRUE  TRUE FALSE FALSE  TRUE

HoursSleep == 6 | HoursSleep == 10 # | means "OR"
#> [1] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE

HoursSleep > 6 & HoursSleep < 10 # & means "AND"
#> [1]  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE

which(HoursSleep == 8)
#> [1] 1 2 3 4
which(HoursSleep > 8)
#> [1] 7
which(HoursSleep >= 8)
#> [1] 1 2 3 4 7

which(HoursSleep == 6 | HoursSleep == 10 ) # | means "OR"
#> [1] 5 6 7

which(HoursSleep > 6 & HoursSleep < 10 ) # & means "AND"
#> [1] 1 2 3 4

WeekEnd <- DaysOfWeek == "Sat" | DaysOfWeek == "Sun"

WeekDay <- !WeekEnd # ! means "NOT"

HoursSleep[WeekDay]
#> [1] 8 8 8 8 6

HoursSleep[WeekEnd]
#> [1]  6 10


cat("These are the hours of sleep on weekdays:", HoursSleep[WeekDay], "\n")
#> These are the hours of sleep on weekdays: 8 8 8 8 6
   # Notice that  \n  is used to create a new line.

Specific elements of a vector can be accessed using square brackets:

HoursSleep[1]
#> [1] 8
HoursSleep[3:5]
#> [1] 8 8 6

HoursSleep[WeekEnd]
#> [1]  6 10

C.2 Statistical functions

Because R is primarily a statistical package and environment, all the basic statistical functions are available, including

mean(): Find the mean of a sample of values. Example: mean( c(1, 2, 3, 4)).
median(): Find the median of a sample of values. Example: median( c(1, 2, 3, 4)).
sd(): Finds the standard deviation of a sample of values. Example: sd( c(1, 2, 3, 4)).
var(): Finds the variance of a sample of values. Example: var( c(1, 2, 3, 4)).
lm(): To fit a linear regression model:

x <- c(1, 2, 3, 4, 5)
y <- c(12, 10, 9, 7, 4)

out <- lm(y ~ x) # Read: 'y as a function of x'
coef(out)
#> (Intercept)           x 
#>        14.1        -1.9
summary(out)
#> 
#> Call:
#> lm(formula = y ~ x)
#> 
#> Residuals:
#>    1    2    3    4    5 
#> -0.2 -0.3  0.6  0.5 -0.6 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)  14.1000     0.6351  22.202  0.00020
#> x            -1.9000     0.1915  -9.922  0.00218
#>                
#> (Intercept) ***
#> x           ** 
#> ---
#> Signif. codes:  
#> 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 0.6055 on 3 degrees of freedom
#> Multiple R-squared:  0.9704, Adjusted R-squared:  0.9606 
#> F-statistic: 98.45 on 1 and 3 DF,  p-value: 0.002178

C.3 Probability and counting functions

the number of combinations of n elements taken k at a time is found using choose(n, k).
\(n!\) is given by factorial(n).
the number of permutations of n elements taken k at a time is found using choose(n, k) * factorial(k).
a list of all combinations of n elements, m at a time, is given by combn(x, m).
\(\Gamma(x)\) is given by gamma(x).

C.4 Vector operations

R is a vectorised system; that is, operations work on all elements of a vector:

x <- 0 : 10
x
#>  [1]  0  1  2  3  4  5  6  7  8  9 10
x + 3
#>  [1]  3  4  5  6  7  8  9 10 11 12 13
2 * x
#>  [1]  0  2  4  6  8 10 12 14 16 18 20

sqrt(x) # The square root function
#>  [1] 0.000000 1.000000 1.414214 1.732051 2.000000
#>  [6] 2.236068 2.449490 2.645751 2.828427 3.000000
#> [11] 3.162278
cos(x)  # The cosine function
#>  [1]  1.0000000  0.5403023 -0.4161468 -0.9899925
#>  [5] -0.6536436  0.2836622  0.9601703  0.7539023
#>  [9] -0.1455000 -0.9111303 -0.8390715
exp( -x ) # The exponential function
#>  [1] 1.000000e+00 3.678794e-01 1.353353e-01
#>  [4] 4.978707e-02 1.831564e-02 6.737947e-03
#>  [7] 2.478752e-03 9.118820e-04 3.354626e-04
#> [10] 1.234098e-04 4.539993e-05

C.5 Plotting functions

Three systems exists for plotting in R, believe it or not. Here, we discuss the base system.

plot() is the basic function for plotting, with many options:

plot(x, y) and plot(y ~ x) both produce a scatterplot, with y on the vertical axis and x on the horizontal axis.
plot(..., type = "l") plots with lines rather than points.
plot(..., lwd = "3") plots with a line width thrice as thick.
plot(..., xlab = "text", ylab = "Info") adds an label to the x and y axes respectively.
plot(..., main = "Title") adds a main title to the plot.
plot(..., col = "green") plots in green rather than the default (black).

plot() starts a new canvas every time it is called. lines() and points() add lines and points respectively to an existing plot. legend() adds a legend to an existing plot.

x <- seq(0, 4, length = 100)
y1 <- dexp(x, rate = 2) # Probability function for an exponential distn

plot(y1 ~ x,
     type = "l", # Use lines, not points
     lwd = 2, # Make lines a bit thicker
     xlab = "Values of x",
     ylab = "Probability function",
     main = "Probability function for\nexponential distribution",
      # NOTE: using  \n  adds a line break, and # is used for comments
     col = "red", 
     las = 1, # Makes the axis labels all horizontal
     xlim = c(0, 4.5), # Changes the displayed limits of the x-axis
     ylim = c(0, 3) ) # Changes the displayed limits on the y-axis

y2 <- dexp(x, rate = 3)
lines( y2 ~ x, # ADD a line to existing point
       lwd = 2,
       col = "blue")

legend("topright", # The location
       lwd = 2,
       col = c("red", "blue"),
       legend = c("Rate = 2",
                  "Rate = 3")
       )

FIGURE C.1: An example plot: the probability function for two exponential distributions

B Using R with distributions

D Selected solutions