## Question

1.) Use the head and summary functions to examine the “mtcars” dataset. What are the attributes in the data set? Which ones are nominal, discrete, continuous?

2.) Indexing is an important part of working with data in R. Using numeric indices, find the horsepower (hp, the forth attribute) of a Datsun 710 (the third car). Also show how you could find this information if you knew only the labels for the object (Datsun 710) and the attribute (hp). What is the horsepower for a Datsun 710?

3.) Let’s examine the attribute “mpg” in more detail. Store the attribute in a vector named “MPG for easy reference. Find the mean, variance, and standard deviation of MPG, and make a boxplot for the variable. Make sure this graph and all future graphs are appropriately labeled! Based on the boxplot, are there any outliers?

4.) Now, let’s look at a histogram for MPG, but use an R library. Install and load the MASS library (include the command to install MASS, even if you have it installed already). Use the truehist function to make a histogram for MPG, using 10 bins for the data. You can use help(truehist) or ?truehist for more information on the function. Based on the histogram, is the data symmetric or skewed? If it is skewed, does it skew left or right?

5.) Now, let’s examine the relationship between Miles per Gallon and Horsepower. Store hp into a vector named HP. Use the plot function the graph HP vs MPG. Do the variables appear to be positively, negatively, or un-correlated?

6.) There appears to be a relationship between MPG and HP, but it does not appear to be linear. Try plotting HP vs the log(MPG). Does this relationship look more linear?

7.) For your final task, perform a simple linear regression using HP and log(MPG). This is not something we covered in class, so you will have to do some research. Make a scatterplot using the variables and add the regression line to it. Change the plotting symbol and color from the defaults for the scatterplot, as well as the color of the line. You may use whatever colors and symbols you want, as long as the graph is still easy to read. Finally, answer the following questions:

a. Is the relationship between HP and MPG significant at alpha = 0.05?

b. What is the regression equation?

c. Do you see any outliers in the data?

## Solution Preview

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# 1.head(mtcars)

summary(mtcars)

# attributes are:

# "mpg" "cyl" "disp" "hp" "drat" "wt" "qsec" "vs" "am" "gear" "carb"

# vs and am are nominal taking only 0 or 1.

# cyl, gear, and carb are discrete count.

# mpg, disp, hp, drat, wt, and qsec are continuous.

# 2.

mtcars[3, 4]

# [1] 93

mtcars["Datsun 710", "hp"]

# [1] 93

# 3.

MPG <- mtcars$mpg

avg <- mean(MPG)

# [1] 20.09062

variance <- var(MPG)

# [1] 36.3241

std <- sd(MPG)

# [1] 6.026948...

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