Question

Researchers measured the blood pressures of 22 students in

two situations: when the students were relaxed and when the students were taking an

important examination. The file

systolic.txt

lists the systolic and diastolic pressures for

each student in each situation. Dataset is available at

systolic_url = "https://mcs.utm.utoronto.ca/~nosedal/data/systolic.txt"

Use R

to answer each of the following questions. You have to show

all your work

to get

full credit.

Answers, even if correct, with no justifications will not receive any

marks

.

a)

Using R

, compute the change in systolic pressure by subtracting systolic pressure when

relaxed from systolic pressure during the exam; call this variable

X

.

b)

Using R

, repeat part a) for diastolic pressure. Call the resulting variable

Y

.

c)

Using R

, make a scatterplot of

Y

versus

X

, fit a regression line to the data and add

this line to your plot. Use: 2 c) your last name as the main title for your plot. (In my

case it would be: 2 c) Nosedal).

Important note. Use

Y

as your response variable and label horizontal and vertical axes.

d) What is the fitted regression model? Provide slope and y-intercept

explicitly

.

Use R

to find them.

e)

Using R

, make a residual plot from the regression in part c). Does this plot call into

question the use of a linear model? Why?

Note. Use:

2 e) your last name

as the main title for your plot. (In my case it would

be:

2 e) Nosedal

).

f) Note the outlier in the residual plot (and on the scatterplot from part c)).

Using

R

, delete the outlier from the data set. Then repeat parts c) and e). Note. Use:

2 f )

your last name

as the main title for your plots. (In my case it would be:

2 f ) Nosedal

).

g) What is the fitted regression model (after the outlier has been removed)? Provide slope

and y-intercept

explicitly

.

Use R

to find them.