1. Match the sentence to one of the following statistics: r , r

-

squared, slope, y

-

intercept, residual,

standard deviation of t

he residual errors. (You may use a statistic more than once.)

(7 pts)

_________________ a

) The percent of variability in y that can be explained by the relationship with x.

_________________ b

) The average distance that all the points in the scatterpl

ot are

from the regression line.

_________________ c

) The amount of increase or decrease in y per 1 unit of x.

_________________ d

) How far a single point is above or below the regression line vertically.

_________________ e

) The predicted y value when x is zero.

_________________ f

) Gives the strength and direction of the correlation

_

________________ g

) The average prediction error.

2

.

Juana

is a biologist studying disease in trees in a local for

est.

She tries

to see if there is a relationship

between temperature (degrees Celsius) and the number of trees that die due to disease. She

also

wants

to predict how many trees may die each year in the forest based on temperature fluctuations.

( 5pts)

_

________________ a

)

Which variable

should be

the explanatory variable (x)?

(Numbe

r of trees that die or the temperature in degrees Celsius)

_________________ b

)

Which variable should be the response variable (y)?

(Numbe

r of trees that die or the temperature in degrees Celsius)

_________________ c

)

Give two confounding variables that may influence the death

of trees

other tha

n temperature.

------------------------------

__________________

d)

Juana

is hoping to prove

that global warming (higher temperatures) cause

trees to die.

If the data showed a strong correla

tion be

tween tempe

rature

and the number of trees that die

, would this prove that

global warming causes

trees to die

?

(yes or no)

_________________________________________________

____e) Explain your answer to letter "d".

3

. Match the correlation coefficient

s

(r)

with their

scatterplot

s

.

(

Each r valu

e corresponds to only one

graph.)

r =

-

0.68,

r =

-

0.96

, r = +0.93 , r =

-

0.81

Then describe the

strength

(weak or moderate or strong or none) and

direction

(positive or negative) of

the correlation.

( 8 pts.)

a)

b)

c)

d)

4

. Use the following formulas to compute the slope

and y

-

intercept

for t

he regression line.

Show your work and

Round your answers to the hundredths place.

(6pts.)

Correlation Coefficient

r = +0.842

Mean

Standard Deviation

(x)

Explanatory Variable

23.9

x

5.7

x

s

(y)

Response Variable

286.4

y

33.8

y

s

a)

slope :

y

x

rs

s

Slope = _____________________

b)

y-intercept :

( )

ymx

Y

-

Intercept = _____________________

(#5

-

20

)

An NBA basketball announcer reported that there has been

an increase in scoring in the NBA

over the last 18 years. To study this we looked

up the average number of points scored in the

NBA over the last 18 seasons (1999

to 2017).

Here is the Statcrunch

printout.

Correlation

Statistics

x =

Years since

1998

y = NBA Average Points Scored Per Year

r

+

0.857

Regression

:

Regression equation Y = 93.6850 + 0.5530

x

r

2

0

.734

Standard Deviation of the Residual Errors

= 1.8299

5.

Multiple Choice:

The cor

relation coefficient was +0.857

and the scatterplot is given above.

Which of

the following best describes the Scatterplot and the correlation coefficient R.

(Circle one)

(2 pts.)

a.

There is weak positive

correlation

between the year and points

.

b.

There is strong positive

correlation

betwe

en the year and points

.

c.

There is no

correlation

between the year and points

.

6. Look at the scatterplot. Estimate the scope of the x

-

values and put your answer below.

Just give approximate values.

( 4 pts.)

________________

Number of Years sinc

e 1998

___________________

7

.

Multiple Choice

: T

he x variable is the number of years

and the y variable is the points per game

.

The

slope of the regression line was

+0.5530

.

Which of the following is a correct description of the meaning

of this slope?

(Circle one)

( 2pts)

a.

For every 1 point increase, the years are increasing 0.5330

.

b.

The average points scored are increasing 0.5330

on average

per year

.

c.

The points in

the scatt

erplot are 0.5330 points

below the regression line.

8

.

Multiple Choice:

T

he x variable is the number of years and the y variable is the points per game

.

The

Y

-

intercept

of the regression line was

93.685

.

Which of the following is a correct descript

ion

of the

meaning of the Y

-

intercept

?

(Circle one)

( 2 pts.)

a.

The predicted number of points per game in year zero (1998) was 93.685 points per game.

b.

For every 1 year increase the

numbers of points are

increasing 93.685 points per game.

c.

The points in the

scatterplot are 93.685 from the regression line.

9

.

Multiple Choice:

Which of the following is

not

a correct interpretation of the r

-

squared value?

(Circle one)

(2 pts.)

Perce

nt of variability in average points scored that can be explained by the

linear

relationship with years

.

The years and average points scored have no relationship

.

There is a strong relati

onship between the years and average points scored.

10

. Convert the R

-

squared of 0.734 into a percentage.

( 2pts.)

________________

1

1

.

List three confounding variables that might

influence the number of

points

teams score other than time

?

( 3 pts.)

1.

---------------------------

2.

---------------------------

3.

________________

12

. Does this study p

rove that time causes the average points per game

to increase

? (Yes or No)

( 2 pts.)

________________

13

.

Multiple Choice:

The stan

dard deviation of the residual errors

is 1.8299 points per game

.

Which of the following is

not

a correct interpretation of the standard deviation of the residuals?

(Circle one)

(2

p

ts)

a.

Average

vertical distance that points are from the regression line is

1.8299 points per game.

b.

If w

e try to predict the

points per game

with the regression line

formula

, our prediction could

have an average error of

1.8299 points per game

.

c.

The slope o

f the regression line is 1.8299

above the y intercept.

Residual Plot

________________ 14

.

Does the Residual Plot

above

show a curved pattern

?

(yes or no)

(2 pts)

Histogram of the Residuals

________________ 15

.

Is the Histogram of the Residuals

shown above

bell shaped? (Yes or No)

(2 pts.)

________________ 16

.

Is t

he Hi

stogram of the centered at

zero? (Yes

or No)

(2 pts.)

Correlation

Statistics

x =

Years since

1998

y = NBA Average Points Scored Per Year

r

+0.857

Regression

:

Regression equation Y = 93.6850 + 0.5530

x

r

2

0

.734

Standard Deviation of the Residual Errors

= 1.8299

________________ 17

. Use your calculator and the regressi

on equation below to predict the points

per game at the end of the season this year (year 19).

(Plug in 19 for X and find Y

.)

Show work. ( 4pts.)

Y = 93.6850 + 0.5530

X

________________ 18

.

How far off could our

points per game

prediction be on average

(prediction error)?

(No calculation is needed

.

)

( 3 pts)

________________

19

.

Will this formula give an accurate prediction

of the points per game in

the year 2055 (year 56)

?

(Yes or No)

( 2 pts.)

20. Explain your answer to #19.

(

2pts.)

________________________________________________

Correlation

Statistics

x =

Years since

1998

y = NBA Average Points Scored Per Year

r

+0.857

Regression

:

Regression equation Y = 93.6850 + 0.5530

x

r

2

0

.734

Standard Deviation of the Residual Errors

= 1.8299

________________ 17

. Use your calculator and the regressi

on equation below to predict the points

per game at the end of the season this year (year 19).

(Plug in 19 for X and find Y

.)

Show work. ( 4pts.)

Y = 93.6850 + 0.5530

X

________________ 18

.

How far off could our

points per game

prediction be on average

(prediction error)?

(No calculation is needed

.

)

( 3 pts)

________________

19

.

Will this formula give an accurate prediction

of the points per game in

the year 2055 (year 56)

?

(Yes or No)

( 2 pts.)

20. Explain your answer to #19.

(

2pts.)

________________________________________________