MATH $4753$ Laboratory $2$

Introduction to R and Chapter $2$

In this lab you will learn the basics of R$.$ This program is free and you are encouraged to

obtain a copy for your Mac, PC or Linux machine. Install it and then download and install

R studio $($this is a nice front end to R and is also free$).$

Objectives

In this lab you will learn how to:

$1.$ Use the empirical rule

$2.$ Use the Chebyshev rule

$3.$ Transform data to z values

$4.$ Find outliers using z values

Tasks

There are many IDE$$s $($integrated development environment$)$ we could use in conjunction with R$,$ however

we will use Rstudio for all of the course.

All output must be made by using an RMD document knit into an html file. Save and place in the dropbox

when completed.

$$ Task $1$

o Download from CANVAS the zipped data files, $$Dataxls$$

o Unzip the contents into a directory on your desktop $($call it LAB$2)$

o Download the file $$lab$2.$r$$

o Place this file with the others in LAB$2.$

o Start Rstudio

o Open $$lab$2.$r$$ from within Rstudio.

o Go to the $$session$$ menu within Rstudio and $$set working directory$$ to where the source

files are located.

o Obtain the working directory by issuing the command getwd$()$:

$$ Task $2$

o Find the file $$EPAGAS$.$xls$$ inside LAB$2$

o Open it in Excel

o Save As type CSV$($comma delimited$)*.$csv$$

o Use read.table$(),$ read.csv$()$ or the Rstudio menu to read the data into

R $($or any other method available$),$ this function will already be available within the script

lab$2.$r which you have opened in Rstudio.

o Obtain the first six lines of the data using $$head$()$ :

$$ Task $3$

o Make the object mpg$,$ the number of miles per gallon vector.

o If $=()$

$,$ then $=0$ and $2$

$=1.$ Transform the mpg variable to z and verify these

results.

o Using z$,$ find the values of mpg that are possible outliers.

o Using z$,$ find the values of mpg that defined as outliers.

o Using the lattice package construct a dotplot with colors, Red$=$outlier, Blue$=$possible

outlier. $($NB $$ read the instructions in the lab$2.$r file for installing the package$)$

$$ Task $4$

o Make a boxplot of the mpg variable

$$ Make the box black

$$ Put a notch where the median goes

$$ Put a title on the graph.

$$ Make the plot horizontal.

o Using Chebyshev$$s theorem predict the proportion of data within $2$ standard deviations of

the mean of the mpg data.

o Use R to calculate the exact proportion within $2$ standard deviation of the mean.

o Does Chebyshev agree with the data?

o Now use the empirical rule, what proportion $($according to the rule$)$ of the data should be

within $2$ standard deviations of the mean?

o How well does it correspond?

o Is the Empirical rule valid in this case? Why?