Question 1

Taxi tires A taxi company monitoring the safety of its cabs kept track of the number of
miles tires had been driven (in thousands) and the depth of the tread remaining (in mm).
Their data are displayed in the scatterplot. They found the equation of the least squares regression line to be tread $= 36 - 0.6$ miles, with $r ^ { 2 } = 0.74$.

a. Draw the line of best fit on the graph. (Show your method clearly.)
b. What is the explanatory variable?
c. The correlation $r =$
d. Describe the association in context.
e. Explain (in context) what the slope of the line means.
f. Explain (in context) what the $y$-intercept of the line means.
g. Explain (in context) what $R ^ { 2 }$ means.
h. In this context, what does a negative residual mean?

Accepted Answer

The answer of Taxi tires A taxi company monitoring the...

Question 2

Computer output in the scenario described in problem #8 reports that $s = 2.3$ . Which is the correct
Interpretation of this value?

Accepted Answer

The value $s = 2.3$ typically represents the standard deviation of the residuals, or the average prediction error of the regression line.

Question 3

A regression equation is found that predicts the increased cost of a home owner's electricity bill given the number of holiday lights they put on the outside of their house. The equation is dollars = $2.5 + 0.02$ (light). If a house has 400 lights and a $\$ 15$ increase in their electricity cost, find their residual.

Accepted Answer

The answer of A regression equation is found that predicts...

Question 4

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 5

Time Wasted A group of students decide to see if there is link between wasting time on the
internet and GPA. They don't expect to find an extremely strong association, but they're
hoping for at least a weak relationship. Here are the findings. $$\begin{array} { l | l | l | } 
\hline \text { linear regression results: } & & \
\text { Dependent Variable: GPA } & \
\text { Sample size: } 10 \
\text { R (correlation coefficient) } = - 0.37199274 & & \
\text { R-sq } = 0.1383786 & & \
s = 0.85365134 & & \
\hline \text { Parameter } & \text { Estimate } & \text { Std. Err. } \
\hline \text { Intercept } & 4.06191 & 0.74405 \
\hline \text { Hours/week } & - 0.0297 & 0.02616 \
\hline & & \
\hline
\end{array}$$ 
a. How strong is the relationship the students found? Describe in context with statistical
justification.
One student is concerned that the relationship is so weak, there may not actually be any
relationship at all. To test this concern, he runs a simulation where the 10 GPA's are
randomly matched with the 10 hours/week. After each random assignment, the correlation
is calculated. This process is repeated 100 times. Here is a histogram of the 100 correlations.
The correlation coefficient of -0.371 is indicated with a vertical line.  
b. Do the results of this simulation confirm the suspicion that there may not be any
relationship? Refer specifically to the graph in your explanation.

Accepted Answer

The answer of Time Wasted A group of students decide...

Question 6

If $r = - 0.4$ for the relationship between the time of day and amount of coffee in an office worker's mug, which are true?
I. $r ^ { 2 } = - 16 \%$
II. There is a linear relationship between time and amount of coffee.
III. $16 \%$ of the variability is correctly predicted by time of day.

Accepted Answer

The answer of If $r = - 0.4$ for the...

Question 7

This regression analysis examines the relationship between the number of years of formal
Education a person has and their annual income. According to this model, about how much more
Money do people who finish a 4-year college program earn each year, on average, than those with
Only a 2-year degree? Dependent variable is Income
R-squared $= 25.8 \%$
$\mathrm { s } = 3888$ with 57 degrees of freedom
$\begin{array} { l c c } \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } \ \text { Constant } & 3984.45 & 6600 \ \text { Education } & 2668.45 & 600.1 \end{array}$

Accepted Answer

The answer of This regression analysis examines the relationship between...

Question 8

A regression model examining the amount of distance a long distance runner runs (in miles) to
Predict the amount of fluid the runner drinks (ounces) has a slope of 4.6. Which interpretation is
Appropriate?

Accepted Answer

The slope of 4.6 indicates that for every additional mile run, the runner is predicted to drink 4.6 more ounces of fluid.

Question 9

High Score The longer you play a video game, the higher score you can usually achieve.
An analysis of a popular game found the following relationship between the hours a
player has played a game and their corresponding high score on that game. Dependent variable is High Score
R-squared $= 76.5 \%$
$s = 383.3$ with 89 degrees of freedom
$\begin{array} { l c c } \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } \ \text { Constant } & 524.8 & 145.3 \ \text { Hours } & 2498.8 & 324.5 \end{array}$ 
a. Write the regression equation and define the variables of your equation in context.
b. Interpret the slope in context.
c. Interpret the y-intercept in context.
d. Interpret s in context.
e. What is the correlation coefficient? Interpret this value in context.

Accepted Answer

The answer of High Score The longer you play a...

Question 10

researcher studied the relationship between family income and amount of money spent on an
Automobile. She calculated that $R ^ { 2 } = 45 \%$
Which is the correct interpretaion?

Accepted Answer

R², or the coefficient of determination, indicates the proportion of the variance in the dependent variable (car price) that is predictable from the independent variable (income). Thus, 45% of the variability in car price can be explained by using income.

Question 11

If a data set has a relationship that is best described by a linear model, than the residual plot will

Accepted Answer

A residual plot with no pattern and a correlation near 0 indicates that a linear model is appropriate for the data set, as it suggests that the linear model has captured the underlying relationship well.

Question 12

We can use the length of a man's hand span to predict his height, with a correlation coefficient of $r$ $= 0.60$. If change our measurements from $\mathrm { cm }$ to $\mathrm { m }$, the new correlation will be

Accepted Answer

The correlation coefficient $r$ is a unitless measure of the strength and direction of a linear relationship between two variables. Changing the units of measurement does not affect the value of $r$.

Question 13

Associations For each pair of variables, indicate what association you expect: positive
linear(+), negative linear(-), curved(C), or none(N).
a. the number of hours in the sun; the number of mold cultures on a piece of bread
b. the number of hours a store is open; the number of sales the store has
c. the number of hours you practice golf; your golf score
d. the price of gasoline; the number of families that take summer road trips
e. the size of a front lawn; the number of children who live in the house

Accepted Answer

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

Question 14

A silly psychology student gathers data on the shoe size of 30 of his classmates and their GPA's.
The correlation coefficient between these two variables is most likely to be

Accepted Answer

Shoe size and GPA are unrelated variables, so the correlation coefficient is likely to be near 0, indicating no linear relationship.

Question 15

Email At CPU every student gets a college email address. Data collected by the college
showed a negative association between student grades and the number of emails the
student sent during the semester.
a. Briefly explain what "negative association" means in this context.
b. After seeing this study the college proposes trying to improve academic performance by
limiting the amount of email students can send through the college address. As a
statistician, what do you think of this plan? Explain briefly.

Accepted Answer

The answer of Email At CPU every student gets a...

Question 16

The relationship between the longevity of an animal's life and its gestation time is 0.70. If an animal
Is one standard deviation below average in life expectancy, the gestation time is predicted to be
__?__ below average.

Accepted Answer

The answer of The relationship between the longevity of an...

Question 17

Car commercials A car dealer investigated the association between the number of TV
commercials he ran each week and the number of cars he sold the following weekend. He
found the correlation to be r = 0.56. During the time he collected the data he ran an average
of 12.4 commercials a week with a standard deviation of 1.8, and sold an average of 30.5
cars with a standard deviation of 4.2. Next weekend he is planning a sale, hoping to sell 40
cars. Create a linear model to estimate the number of commercials he should run this week.
Write a sentence explaining your recommendation.

Accepted Answer

The answer of Car commercials A car dealer investigated the...

Question 18

Associations For each pair of variables, indicate what association you expect: positive
linear(+), negative linear(-), curved(C), or none(N).
a. the number of miles a student lives from school; the student's GPA
b. a person's blood alcohol level; time it takes the person to solve a maze
c. weekly sales of hot chocolate at a Montana diner; the number of auto accidents that week
in that town
d. the price charged for fund-raising candy bars; number of candy bars sold
e. the amount of rainfall during growing season; the crop yield (bushels per acre)

Accepted Answer

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

Question 19

Make a scatterplot and describe the association between the size of the diamond (carat) and
the cost (in US dollars).

Accepted Answer

The answer of Make a scatterplot and describe the association...

Question 20

Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from
500 to 1000, how much do we predict he will increase his electric bill by?

Accepted Answer

The answer of Using the equation in number #8 again,...

Quiz 8: Regression, Associations, and Predictive Modeling

Computer output in the scenario described in problem #8 reports that $s = 2.3$ . Which is the correct Interpretation of this value?

If $r = - 0.4$ for the relationship between the time of day and amount of coffee in an office worker's mug, which are true? I. $r ^ { 2 } = - 16 \%$ II. There is a linear relationship between time and amount of coffee. III. $16 \%$ of the variability is correctly predicted by time of day.

A regression model examining the amount of distance a long distance runner runs (in miles) to Predict the amount of fluid the runner drinks (ounces) has a slope of 4.6. Which interpretation is Appropriate?

researcher studied the relationship between family income and amount of money spent on an Automobile. She calculated that $R ^ { 2 } = 45 \%$ Which is the correct interpretaion?

If a data set has a relationship that is best described by a linear model, than the residual plot will

We can use the length of a man's hand span to predict his height, with a correlation coefficient of $r$ $= 0.60$ . If change our measurements from $\mathrm { cm }$ to $\mathrm { m }$ , the new correlation will be

A silly psychology student gathers data on the shoe size of 30 of his classmates and their GPA's. The correlation coefficient between these two variables is most likely to be

The relationship between the longevity of an animal's life and its gestation time is 0.70. If an animal Is one standard deviation below average in life expectancy, the gestation time is predicted to be ? below average.

Make a scatterplot and describe the association between the size of the diamond (carat) and the cost (in US dollars).

Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from 500 to 1000, how much do we predict he will increase his electric bill by?

Quiz 8: Regression, Associations, and Predictive Modeling

Computer output in the scenario described in problem #8 reports that s=2.3s = 2.3s=2.3 . Which is the correct Interpretation of this value?

A regression model examining the amount of distance a long distance runner runs (in miles) to Predict the amount of fluid the runner drinks (ounces) has a slope of 4.6. Which interpretation is Appropriate?

researcher studied the relationship between family income and amount of money spent on an Automobile. She calculated that R2=45%R ^ { 2 } = 45 \%R2=45% Which is the correct interpretaion?

If a data set has a relationship that is best described by a linear model, than the residual plot will

We can use the length of a man's hand span to predict his height, with a correlation coefficient of rrr =0.60= 0.60=0.60 . If change our measurements from cm\mathrm { cm }cm to m\mathrm { m }m , the new correlation will be

A silly psychology student gathers data on the shoe size of 30 of his classmates and their GPA's. The correlation coefficient between these two variables is most likely to be

The relationship between the longevity of an animal's life and its gestation time is 0.70. If an animal Is one standard deviation below average in life expectancy, the gestation time is predicted to be __?__ below average.

Make a scatterplot and describe the association between the size of the diamond (carat) and the cost (in US dollars).

Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from 500 to 1000, how much do we predict he will increase his electric bill by?

Computer output in the scenario described in problem #8 reports that $s = 2.3$ . Which is the correct Interpretation of this value?

researcher studied the relationship between family income and amount of money spent on an Automobile. She calculated that $R ^ { 2 } = 45 \%$ Which is the correct interpretaion?

We can use the length of a man's hand span to predict his height, with a correlation coefficient of $r$ $= 0.60$ . If change our measurements from $\mathrm { cm }$ to $\mathrm { m }$ , the new correlation will be

The relationship between the longevity of an animal's life and its gestation time is 0.70. If an animal Is one standard deviation below average in life expectancy, the gestation time is predicted to be ? below average.