Question 1

On the axes below, sketch a scatterplot described:
a. a strong negative association  
b. a strong association but r is near 0  
c. a weak but positive association

Accepted Answer

a.

b.

c.

Question 2

A common objective for many school administrators is to increase the number of students
taking SAT and ACT tests from their school. The data from each state from 2003 are
reflected in the scatterplot.  
a. Write a few sentences describing the association.
b. Estimate the correlation. $r =$________ 
c. If the point in the top left corner (4, 1215) were removed, would the correlation become
stronger, weaker, or remain about the same? Explain briefly.
d. If the point in the very middle (38, 1049) were removed, would the correlation become
stronger, weaker, or remain about the same? Explain briefly.

Accepted Answer

a. There is a moderate, negative, linear association between the percent of students
taking the SAT test and the total SAT score. It appears that the states with a larger
percentage of students taking the SAT test have lower average total scores.
b. r = -0.76 (answers between -0.6 and -0.9 are acceptable)
c. If the point in the top left corner (4, 1215) were removed, the correlation would
become stronger because the remaining points show a pattern with slightly less
scatter.
d. If the point in the very middle (38, 1049) were removed, the correlation would
remain about the same; this point does not contribute much to the scatter.

Question 3

A consumer group collected information on HDTVs . They created a linear model to estimate the
Cost of an HDTV (in $) based on the screen size (in inches). Which is the most likely value of the
Slope of the line of best fit?
A) 70
B) 0.70
C) 7000
D) 7
E) 700

Accepted Answer

The slope of the line of best fit represents the change in cost for each additional inch of screen size. A slope of 70 suggests a reasonable increase in cost per inch for HDTVs.

Question 4

Identify what is wrong with each of the following statements:
a. The correlation between Olympic gold medal times for the 800m hurdles and year is
-0.66 seconds per year.
b. The correlation between Olympic gold medal times for the 100m dash and year is -1.37.
c. Since the correlation between Olympic gold medal times for the 800m hurdles and 100m
dash is -0. 41, the correlation between times for the 100m dash and the 800m hurdles is
+0.41.
d. If we were to measure Olympic gold medal times for the 800m hurdles in minutes
instead of seconds, the correlation would be $- 0.66 / 60 = - 0.011$

Accepted Answer

The answer of Identify what is wrong with each of...

Question 5

After conducting a survey at a pet store to see what impact having a pet had on the
condition of the yard, a news reporter stated "There appears to be a strong correlation
between the owning a pet and the condition of the yard." Comment on this observation.

Accepted Answer

The answer of After conducting a survey at a pet...

Question 6

The following scatterplot shows the relationship between the time (in seconds) it took men
to run the 1500m race for the gold medal and the year of the Olympics that the race was
run in: 
a. Write a few sentences describing the association.
b. Estimate the correlation. $r =$

Accepted Answer

The answer of The following scatterplot shows the relationship between...

Question 7

The auto insurance industry crashed some test vehicles into a cement barrier at speeds of 5 to 25
Mph to investigate the amount of damage to the cars. They found a correlation of r = 0.60 between
Speed (MPH) and damage ($). If the speed at which a car hit the barrier is 1.5 standard deviations
Above the mean speed, we expect the damage to be _?__ the mean damage.
A) 0.90 SD above
B) 1.5 SD above
C) equal to
D) 0.36 SD above
E) 0.60 SD above

Accepted Answer

The correlation coefficient is 0.60, which means that there is a moderate positive correlation between speed and damage. This means that as speed increases, damage also tends to increase. The mean speed is not given, but we are told that the speed at which a car hit the barrier is 1.5 standard deviations above the mean speed. This means that the speed is 1.5 * SD above the mean. We can use the correlation coefficient to predict the amount of damage that we would expect to see at this speed. The expected damage is equal to the mean damage plus 0.60 * 1.5 * SD = 0.90 SD above the mean.

Question 8

Match each graph with the appropriate correlation coefficient. ______$ 0.98 $_____$ 0.73 $_____-$ 0.09 $______$ -0.99 $
A.

B.

C.

D.

Accepted Answer

The answer of Match each graph with the appropriate correlation...

Question 9

Match the following descriptions with the most likely correlation coefficient.
____ The number of hours you study and your exam score.
____ The number of siblings you have and your GPA.
____ The number of hours you practice a task and the number of minutes it takes you to
complete it.
____ The number of hours you use a pencil and its length.
A. -0.78
B. 0.13
C. 0.46
D. 0.89

Accepted Answer

The answer of Match the following descriptions with the most...

Question 10

One of your classmates is reading through the program for Friday night''s football game.
Among other things, the program lists the players'' positions and their weights. Your
classmate comments, "There is a strong correlation between a player's position and their
weight."
a. Explain why your classmate's statement is in error.
b. What other variable might be listed in the program that could be used to correctly
identify a correlation with weight?

Accepted Answer

The answer of One of your classmates is reading through...

Question 11

The following scatterplot shows a relationship between $x$ and $y$ that results in a correlatior coefficient of $r = 0$. Explain why $r = 0$ in this situation even though there appears to be a strong relationship between the $x$ and $y$ variables.

Accepted Answer

The answer of The following scatterplot shows a relationship between...

Question 12

A school board study found a moderately strong negative association between the number
of hours high school seniors worked at part-time jobs after school hours and the students'
grade point averages.
a. Explain in this context what "negative association" means.
b. Hoping to improve student performance, the school board passed a resolution urging
parents to limit the number of hours students be allowed to work. Do you agree or
disagree with the school board's reasoning. Explain.

Accepted Answer

The answer of A school board study found a moderately...

Question 13

After conducting a survey of his students, a professor reported that "There appears to be a
strong correlation between grade point average and whether or not a student works."
Comment on this observation.

Accepted Answer

The answer of After conducting a survey of his students,...

Question 14

Researchers studying growth patterns of children collect data on the heights of fathers and sons.
The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely
To be . . .
A) near +1.0
B) somewhat greater than 1.0
C) near -1.0
D) near +0.7
E) near 0

Accepted Answer

The correlation between fathers' heights and their sons' heights is likely to be positive and moderately strong, around +0.7, indicating a tendency for taller fathers to have taller sons, but not a perfect correlation.

Question 15

A researcher notes that there is a positive correlation between the temperature on a
summer day and the number of bees that he can count in his garden over a 5-minute time
span.
a. Describe what the researcher means by a positive correlation.
b. If the researcher calculates the correlation coefficient using degrees Fahrenheit instead of
Celsius, will the value be different?

Accepted Answer

The answer of A researcher notes that there is a...

Question 16

One your classmates is working on a science project for a unit on weather. She tracks the
temperature one day, beginning at sunrise and finishing at sunset. Given that you are
know for being the stats expert, she asks you about calculating the correlation for her data.
What is the best advice you could give her?

Accepted Answer

The answer of One your classmates is working on a...

Question 17

After conducting a marketing study to see what consumers thought about a new tinted
contact lens they were developing, an eyewear company reported, "Consumer satisfaction
is strongly correlated with eye color." Comment on this observation.

Accepted Answer

The answer of After conducting a marketing study to see...

Question 18

Researchers investigating the association between the size and strength of muscles
measured the forearm circumference (in inches) of 20 teenage boys. Then they measured
the strength of the boys' grips (in pounds). Their data are plotted.  
a. Write a few sentences describing the association.
b. Estimate the correlation. r = ________
c. If the point in the lower right corner (at about 14" and 38 lbs.) were removed, how would
the correlation become stronger, weaker, or remain about the same?
d. If the point in the upper right corner (at about 15" and 75 lbs.) were removed, would the
correlation become stronger, weaker, or remain about the same?

Accepted Answer

The answer of Researchers investigating the association between the size...

Question 19

A study by a prominent psychologist found a moderately strong positive association
between the number of hours of sleep a person gets and the person's ability to memorize
information.
a. Explain in the context of this problem what "positive association" means.
b. Hoping to improve academic performance, the psychologist recommended the school
board allow students to take a nap prior to any assessment. Discuss the psychologist's
recommendations.

Accepted Answer

The answer of A study by a prominent psychologist found...

Question 20

The correlation between $$X \text { and } Y \text { is } r = 0.35 \text {. If we double each } X \text { value }$$ alue, decrease each Y by 0.20, and
Interchange the variables (put X on the Y-axis and vice versa), the new correlation
A) is 0.50
B) is 0.35
C) is 0.90
D) cannot be determined.
E) is 0.70

Accepted Answer

The answer of The correlation between \[X \text { and...

Quiz 8: Regression, Associations, and Predictive Modeling

On the axes below, sketch a scatterplot described: a. a strong negative association b. a strong association but r is near 0 c. a weak but positive association

A consumer group collected information on HDTVs . They created a linear model to estimate the Cost of an HDTV (in $) based on the screen size (in inches) . Which is the most likely value of the Slope of the line of best fit?

After conducting a survey at a pet store to see what impact having a pet had on the condition of the yard, a news reporter stated "There appears to be a strong correlation between the owning a pet and the condition of the yard." Comment on this observation.

The following scatterplot shows the relationship between the time (in seconds) it took men to run the 1500m race for the gold medal and the year of the Olympics that the race was run in: a. Write a few sentences describing the association. b. Estimate the correlation. $r =$

Match each graph with the appropriate correlation coefficient. ____ $0.98$ _ $0.73$ _- $0.09$ ____ $-0.99$ A. B. C. D.

The following scatterplot shows a relationship between $x$ and $y$ that results in a correlatior coefficient of $r = 0$ . Explain why $r = 0$ in this situation even though there appears to be a strong relationship between the $x$ and $y$ variables.

After conducting a survey of his students, a professor reported that "There appears to be a strong correlation between grade point average and whether or not a student works." Comment on this observation.

Researchers studying growth patterns of children collect data on the heights of fathers and sons. The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely To be . . .

After conducting a marketing study to see what consumers thought about a new tinted contact lens they were developing, an eyewear company reported, "Consumer satisfaction is strongly correlated with eye color." Comment on this observation.

The correlation between $X \text { and } Y \text { is } r = 0.35 \text {. If we double each } X \text { value }$ alue, decrease each Y by 0.20, and Interchange the variables (put X on the Y-axis and vice versa) , the new correlation