STAT 345 - Homework 0

This is a very quick/basic introduction to R. We will be using R more heavily in the second half of this course, but for now I just want you to be able to produce some very simple plots.

I’ll cover R in more detail later in the year, but if anybody is interested in learning more the following link has some good resources.

https://www.rstudio.com/online-learning/#r-programming

Using R as a Calculator

# Add two numbers
2 + 3

## [1] 5

# Multiply two numbers
2 * 3

## [1] 6

# Exponents
2^3

## [1] 8

# Be careful with parentheses
2 + (3 * 4)

## [1] 14

(2 + 3) * 4

## [1] 20

# Other built in functions
exp(1)

## [1] 2.718282

log(10) #Careful! This is natural log

## [1] 2.302585

sin(2*pi)

## [1] -2.449294e-16

floor(4.5)

## [1] 4

sqrt(9)

## [1] 3

factorial(4)

## [1] 24

Creating Variables

You can also store numbers in variables for later use.

Side note: Although R allows = as an assigmnet operator, I will usually use <-, as they do slightly different things. Ask me if you want more details.

#Create a variable named x
x <- 2
x

## [1] 2

#Create a variable named y
y <- x^2
y

## [1] 4

#Create a variable named z
z <- x + y
z

## [1] 6

The Curve Function

R is a very nice language for creating graphs. I highly recommend looking into ggplot2, as it produces beautiful/modern/publishable graphs quite easily. Base R has many simple to use functions for plotting such as, plot(), hist(), points(), lines() etc. For now though, I want us to become comfortable with the curve() function.

Lets try to plot the function

f (x) = 2 x^{2}

$f(x) = 2x^2$

# Plot the function
curve(2*x^2) #Plots from 0 to 1 by default

# Change the limits of the plot
curve(2*x^2, from=-4, to=4)

# Make the plot pretty
curve(2*x^2, from=-4, to=4,
      col='blue', lwd=2, xlab='x', ylab='f(x)', main='This is a Title')

The Plot Function (Optional)

I chose to cover the curve function because of it’s simplicity. Another more versatile way of plotting is to use the plot() function.

# Create a vector of x points to plot at
x <- seq(-4, 4, by=1) # Or equivalently, x <- -4:4

# Create vector of y points
y <- 2*x^2

# Use the plot function
plot(x, y, xlab='x', ylab='f(x)', main='Another Plot Title')

The plot function can take a type argument. Some of the options are

‘p’ for points (default)
‘l’ for lines
‘o’ for overlayed points and lines

We can also adjust the color, point type (pch), size (cex) etc. This stuff is all very google-able. (:

# Make plot pretty
plot(x, y, xlab='x', ylab='f(x)', main='Another Plot Title',
     col='blue', pch=21, bg='orange', type='o')

Assignment

Consider the following function.

f (x) = \frac{1}{1 + \exp (5 - x)}

$f(x) = \frac{1}{1+\exp(5-x)}$

Install R and RStudio (See course web-page for link).
Plot this function for values of $x$ between 0 and 10. Label it an play around with some of the style options.
The title of the plot should be your full name.
Email the plot to me. Use copy and paste to put STAT 345 - Homework 0 in the subject line.