Question 1

Which is true?
I. Random scatter in the residuals indicates a model with high predictive power.
II. If two variables are very strongly associated, then the correlation between them will be near +1.0
Or -1.0.
III. The higher the correlation between two variables the more likely the association is based in
Cause and effect.

Accepted Answer

A)  I, II, and III 
B)  I and II 
C)  I only 
D)  II only 
E)  none

Question 2

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 3

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 4

Halloween is a fun night. It seems that older children might get more candy because they can travel further while
trick-or-treating. But perhaps the youngest kids get extra candy because they are so cute. Here are some data that examine
this question, along with the regression output. Dependent Variable: candy
Sample size: 9
$R$ (correlation coefficient) $= \mathbf { 0 . 1 9 5 3 4 4 2 5 }$
$\mathrm { R } - \mathrm { sq } = 0.038159375$
$s = 11.297554$
$\begin{array} { l r r } \text { Parameter } & \text { Estimate } & \text { Std. Err. } \ \text { Intercept } & 13.569231 & 9.0783516 \ \text { Age } & 3.4038462 & 1.0175376 \end{array}$

-The next day, a young girl reveals that her older brother also went trick-or-treating, but
didn't want to admit that he participated. He was added to the data set and these are the
results. Dependent Variable: candy
Sample size: 10
$R$ (correlation coefficient $) = 0.76362369$
$\mathrm { R } - \mathrm { sq } = 0.58312115$
$\mathrm { s } = 12.709041$
$\begin{array} { l r r } \text { Parameter } & \text { Estimate } & \text { Std. Err. } \ \text { Intercept } & 13.569231 & 9.0783516 \ \text { Age } & 3.4038462 & 1.0175376 \end{array}$

Describe the effect of this new candy collector on the regression model.

Accepted Answer

The answer of Halloween is a fun night. It seems...

Question 5

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

The answer of A common objective for many school administrators...

Question 6

Associations For each pair of variables, indicate what association you expect: positive(+), $\text { negative } ( - ) \text {, curved } ( \mathrm { C } ) \text {, or none } ( \mathrm { N } ) \text {. }$ 
a. power level setting of a microwave; number of minutes it takes to boil water
b. number of days it rained in a month (during the summer); number of times you mowed
your lawn that month
c. number of hours a person has been up past a normal bedtime; number of minutes it
takes the person to do a crossword puzzle
d. number of hockey games played in Minnesota during a week; sales of suntan lotion in
Minnesota during that week
e. length of a student's hair; number of credits the student earned last year

Accepted Answer

The answer of Associations For each pair of variables, indicate...

Question 7

Earning power A college's job placement office collected data about students' GPAs and
the salaries they earned in their first jobs after graduation. The mean GPA was 2.9 with a
standard deviation of 0.4. Starting salaries had a mean of $47,200 with a SD of $8500. The
correlation between the two variables was $$r = 0.72$$ 
The association appeared to be linear in
the scatterplot. (Show work)
a. Write an equation of the model that can predict salary based on GPA.
b. Do you think these predictions will be reliable? Explain.
c. Your brother just graduated from that college with a GPA of 3.30. He tells you that based
on this model the residual for his pay is -$1880. What salary is he earning?

Accepted Answer

The answer of Earning power A college's job placement office...

Question 8

Math and Verbal Suppose the correlation between SAT Verbal scores and Math scores is
0.57 and that these scores are normally distributed. If a student's Verbal score places her at
the 90th percentile, at what percentile would you predict her Math score to be?
(SHOW WORK)

Accepted Answer

The answer of Math and Verbal Suppose the correlation between...

Question 9

Which of the following is not a source of caution in regression between two variables?

Accepted Answer

A)  an outlier 
B)  extrapolation 
C)  subgroups with differences 
D)  All of these are potential problems. 
E)  a lurking variable

Question 10

The correlation coefficient between high school grade point average (GPA) and college GPA is
0)560. For a student with a high school GPA that is 2.5 standard deviations above the mean, we
Would expect that student to have a college GPA that is ______ the mean.

Accepted Answer

A)  2.5 SD above 
B)  1.4 SD above 
C)  equal to 
D)  0.56 SD above

Question 11

To achieve linearity, the data was transformed using a square root function of cost. Here are the results and a residual plot. Dependent Variable: sqrt(cost)
s: $0.2141$
$\begin{array} { l r r } \text { Parameter } & \text { coeff } & \text { se } \ \text { Intercept } & 1.1857 & 0.4346 \ \text { height } & 0.1792 & 0.0151 \end{array}$

-Interpret R-sq in the context of this problem.

Accepted Answer

The answer of To achieve linearity, the data was transformed...

Question 12

A regression analysis of students' college grade point averages (GPAs) and their high school GPAs
Found $R ^ { 2 } = 0.311$
11) Which of these is true?
I. High school GPA accounts for 31.1% of college GPA.
II. 31.1% of college GPAs can be correctly predicted with this model.
III. 31.1% of the variance in college GPA can be accounted for by the model

Accepted Answer

A)  I only 
B)  none of these 
C)  II only 
D)  III only 
E)  I and II

Question 13

You are given the following costs to build a square deck for your house: $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Width (ft) } & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \
\hline \text { Cost (\$) } & 150 & 255 & 350 & 500 & 650 & 800 & 1000 & 1200 & 1450 & 1700 & 1950 & 2250 \
\hline
\end{array}$$ 
a. Use re-expressed data to create a model that predicts the cost of the deck based on the
width.
b. Why do you think that your model is appropriate?
c. Find the predicted cost of a square deck that is 10.5 feet wide.
d. Is it reasonable to use this model to predict the cost of a square deck that is 20 feet wide?
Explain.

Accepted Answer

The answer of You are given the following costs to...

Question 14

During a science lab, students heated water, allowed it to cool, and recorded the temperature over time. They computed the
difference between the water temperature and the room temperature. The results are in the table. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Time (in minutes) } & 10 & 20 & 30 & 40 & 50 & 60 \
\hline \text { Difference in temp. (degrees F) } & 68 & 36 & 20 & 10 & 6 & 4 \
\hline
\end{array}$$
-Would it be better for customers for a year to have a negative residual or a positive
residual from this model? Explain.

Accepted Answer

The answer of During a science lab, students heated water,...

Question 15

The residuals plot for a linear model is shown. Which is true?

Accepted Answer

A)  The linear model is no good since some residuals are large. 
B)  The linear model is no good because of the curve in the residuals. 
C)  The linear model is okay because the association between the two variables is fairly strong. 
D)  The linear model is okay because approximately the same number of points are above the line as below it. 
E)  The linear model is no good since the correlation is near 0.

Question 16

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 17

Penicillin Doctors studying how the human body assimilates medication inject some
patients with penicillin, and then monitor the concentration of the drug (in units/cc) in the
patients' blood for seven hours. The data are shown in the scatterplot. First they tried to fit
a linear model. The regression analysis and residuals plot are shown. Dependent variable is:
Concentration
No Selector
R squared $= 90.8 \% \quad$ R squared (adjusted) $= 90.6 \%$
$s = 3.472$ with $43 - 2 = 41$ degrees of freedom

$\begin{array}{llrrr}
\text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \
\text { Regression } & 4900.55 & 1 & 4900.55 & 407 \
\text { Residual } & 494.199 & 41 & 12.0536 &
\end{array}$

$\begin{array}{lllrl}
\text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \
\text { Constant } & 40.3266 & 1.295 & 31.1 & \leq 0.0001 \
\text { Time } & -5.95956 & 0.2956 & -20.2 & \leq 0.0001
\end{array}$

a. Find the correlation between time and concentration.
b. Using this model, estimate what the concentration of penicillin will be after 4 hours.
c. Is that estimate likely to be accurate, too low, or too high? Explain.
Now the researchers try a new model, using the re-expression log(Concentration). Examine
the regression analysis and the residuals plot below. Dependent variable is: LogCnn
No Selector
R squared $= 98.0 \% \quad$ R squared (adjusted) $= 98.0 \%$
$s = 0.0451$ with $43 - 2 = 41$ degrees of freedom

$\begin{array}{llrrr}
\text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \
\text { Regression } & 4.11395 & 1 & 4.11395 & 2022 \
\text { Residual } & 0.083412 & 41 & 0.002034 &
\end{array}$

$\begin{array}{llllc}
\text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \
\text { Constant } & 1.80184 & 0.0168 & 107 & \leq 0.0001 \
\text { Time } & -0.172672 & 0.0038 & -45.0 & \leq 0.0001
\end{array}$ 
  
d. Explain why you think this model is better than the original linear model.
e. Using this new model, estimate the concentration of penicillin after 4 hours.

Accepted Answer

The answer of Penicillin Doctors studying how the human body...

Question 18

When using midterm exam scores to predict a student's final grade in a class, the student would
Prefer to have a

Accepted Answer

A)  negative residual, because that means the students final grade is higher than we would predict with the model. 
B)  residual equal to zero, because that means the student's final grade is exactly what we would predict with the model. 
C)  positive residual, because that means the student's final grade is lower than we would predict with the model. 
D)  positive residual, because that means the student's final grade is higher than we would predict with the model. 
E)  negative residual, because that means the student's final grade is lower than we would predict with the model.

Question 19

Put to Work Some students have to work part time jobs to pay for college expenses. A
researcher examined the academic performance of students with jobs versus those without.
He found a positive association between the number of hours worked and GPA. Explain
what "positive association" means in this context.

Accepted Answer

The answer of Put to Work Some students have to...

Question 20

Education research consistently shows that students from wealthier families tend to have higher
SAT scores. The slope of the line that predicts SAT score from family income is 6.25 points per $1000,
And the correlation between the variables is 0.48. Then the slope of the line that predicts family
Income from SAT score (in $1000 per point) …

Accepted Answer

A)  is 6.25 
B)  is 0.037 
C)  is 13.02 
D)  is 0.16 
E)  is 3.00

Exam 2: Exploring Relationships Between Variables

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.

Math and Verbal Suppose the correlation between SAT Verbal scores and Math scores is 0.57 and that these scores are normally distributed. If a student's Verbal score places her at the 90th percentile, at what percentile would you predict her Math score to be? (SHOW WORK)

Which of the following is not a source of caution in regression between two variables?

The correlation coefficient between high school grade point average (GPA) and college GPA is 0) 560. For a student with a high school GPA that is 2.5 standard deviations above the mean, we Would expect that student to have a college GPA that is ______ the mean.

The residuals plot for a linear model is shown. Which is true?

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.

When using midterm exam scores to predict a student's final grade in a class, the student would Prefer to have a