Question

For the mtcars dataset (in R), comment on how Rear axle ratio is associated with Displacement (cu.in.) and Miles/(US) gallon using the following steps:

1. Draw appropriate scatterplot(s) [Show your code in “R Code” section. Leave “Answer” section blank. Justify your choice of charts in a few sentences in “Comments” section. No screenshots of the charts are required.]

2. Determine correlation coefficient(s) [Show your code in “R Code” section. Show the answer in “Answer” section. Leave “Comments” section blank.]

3. Calculate and plot appropriate regression lines [Show your code in “R Code” section. Leave “R Code” and “Comments” section blank.]

4. Comment on how the variables are associated with each other [Leave “R Code” and “Answer” section blank. Include the phrase “associated” or “not associated” along with a justification in a few sentences in “Comments” section.]

Answer 1

ANSWER::

​R Code:

#data
Mtcars = mtcars
View(mtcars)

#Scatterplot
plot(Mtcars$mpg,Mtcars$disp,main = "Scatter plot between mpg and disp")

#correlation coefficient between mpg and disp
cor(Mtcars$mpg,Mtcars$disp)
#calculate regression coefficient using lm function
lm(Mtcars$disp~Mtcars$mpg)

#Fitted regression line
abline(lm(Mtcars$disp~Mtcars$mpg))

(a)

(b)

Correlation coefficient = -0.8475514

(c)

fitted regression line:

(d)

Using the above-fitted regression line we conclude that mpg is negatively associated with displacement.

Similarly, we can do for the mpg and hp

R code:

# between mpg and hp

#Scatterplot
plot(Mtcars$mpg,Mtcars$hp,main = "Scatter plot between mpg and disp")

#correlation coefficient between mpg and disp
cor(Mtcars$mpg,Mtcars$hp)

#calculate regression coefficient using lm function
lm(Mtcars$hp~Mtcars$mpg)

#Fitted regression line
abline(lm(Mtcars$hp~Mtcars$mpg))

(a)

(b)

correlation coefficient = -0.7761684

(c)

(d)

Using the above-fitted regression line we conclude that mpg is negatively associated with Gross horsepower.

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