Deck 6: Correlation and Linear Regression

Question 1

In discussing how its customers use online services, a bank manager noted "there
seems to be a strong correlation between the use of the online bill paying feature and
gender." Comment on this statement.

Answer 1

There may be an association between the use of online bill paying and gender, but these
variables are both categorical so they cannot be correlated.

Question 2

Analyze scatterplots and correlation coefficients.
The scatterplot shows monthly sales figures (in units) and number of months of
Experience for a sample of salespeople. The correlation between monthly sales and level
Of experience is most likely

A) -.235.
B) 0.
C) .180.
D) -.914.
E) .914.

Answer 2

E

Question 3

Use the following to answer questions 5 - 8.
To determine whether the cash bonus paid by a company is related to annual pay, data
were gathered for 10 account executives at Johnson Financial Group who received cash
bonuses in 2007. The data, scatterplot, and summary statistics are shown below.

Answer 3

.54, which means that 54% of the variability in cash bonuses can be explained by pay.

Question 4

For each of the following scenarios indicate which is the predictor variable and which
is the response variable.
a. A study examined consumption levels of oil and carbon dioxide emissions for a sample
of counties.
b. Data were collected on job performance rating and hours of training for a sample of
employees at a telecommunications repair facility.
c. Salary data as well as years of managerial experience were collected for a sample of
executives in the high tech industry.

Question 5

Use the following to answer questions 5 - 8.
A small independent organic food store offers a variety of specialty coffees. To
determine whether price has an impact on sales, the managers kept track of how many
pounds of each variety of coffee were sold last month. The data, scatterplot and
summary statistics are shown below.
Find the value of R2. Interpret its meaning in this context.

Question 6

Use the following to answer questions 5 - 8.
A small independent organic food store offers a variety of specialty coffees. To
determine whether price has an impact on sales, the managers kept track of how many
pounds of each variety of coffee were sold last month. The data, scatterplot and
summary statistics are shown below.
Using the estimated regression equation,
a. Estimate the monthly sales for a variety of coffee that costs $12 per pound.
b. What is the residual for this estimate?
What does it mean?

Question 7

Assign roles to variables.
A supermarket chain gathers data on the amount they spend on promotional material
(e)g., coupons, etc.) and sales revenue generated each quarter. The predictor variable is

A) sales revenue.
B) amount spent on promotional material.
C) number of coupons offered.
D) supermarket chains.
E) none of the above.

Question 8

Use the following to answer questions 5 - 8.
To determine whether the cash bonus paid by a company is related to annual pay, data
were gathered for 10 account executives at Johnson Financial Group who received cash
bonuses in 2007. The data, scatterplot, and summary statistics are shown below.
Using the estimated regression equation,
a. Estimate the cash bonus for an executive at Johnson Financial earning $82, 613 a year. b. What is the residual for this estimate?
What does it mean?

Question 9

Shown below is a correlation table showing correlation coefficients between stock
price, earnings per share (EPS), and price / earnings (P / E) ratio for a sample of 19 publicly
traded companies.
Correlations: Stock Price, EPS, PE
a. What is the correlation between stock price and EPS? Interpret.
b. What is the correlation between stock price and PE? Interpret.
c. What is the correlation between EPS and PE? Interpret.

Question 10

Assign roles to variables.
A study examined consumption levels of oil and carbon dioxide emissions for
Sample of counties. The response variable in this study is

A) oil.
B) oil consumption.
C) carbon dioxide emissions.
D) countries.
E) none of the above.

Question 11

The following scatterplot shows monthly sales figures (in units) and number of
months of experience on the job for a sample of 19 salespeople.
a. Describe the association between monthly sales and level of experience.
b. Do these data satisfy the conditions for computing a correlation coefficient? Explain.
c. Estimate the correlation.

Question 12

Shown below is a correlation table showing correlation coefficients between
population (in millions), PC adoption, and cell phone adoption for a sample of 16
countries.
Correlations: PC Adoption, Cell Phone Adoption, Population (mill)
a. What is the correlation between PC adoption and population? Interpret.
b. What is the correlation between cell phone adoption and population? Interpret.
c. What is the correlation between PC adoption and cell phone adoption? Interpret.

Question 13

Use the following to answer questions 5 - 8.
A small independent organic food store offers a variety of specialty coffees. To
determine whether price has an impact on sales, the managers kept track of how many
pounds of each variety of coffee were sold last month. The data, scatterplot and
summary statistics are shown below.
Estimate the linear regression model that relates the response variable (monthly sales)
to the predictor variable (price per pound).
a. Find the slope of the regression line.
b. Find the intercept of the regression line.
c. Write the equation of the linear model.

Question 14

Use the following to answer questions 5 - 8.
A small independent organic food store offers a variety of specialty coffees. To
determine whether price has an impact on sales, the managers kept track of how many
pounds of each variety of coffee were sold last month. The data, scatterplot and
summary statistics are shown below.
Comment on whether each of the following conditions for correlation / linear
regression is met.
a. Quantitative variable condition.
b. Linearity condition.
c. Outlier condition.

Question 15

In commenting on the increase in home foreclosures, a news reporter stated "there
appears to be a strong correlation between home foreclosures and job loss of the head of
household." Comment on this statement.

Question 16

Analyze scatterplots and correlation coefficients.
The scatterplot shows monthly sales figures (in units) and number of months of
Experience for a sample of salespeople. The association between monthly sales and level
Of experience can be described as

A) positive and weak.
B) negative and weak.
C) negative and strong.
D) positive and strong.
E) nonlinear.

Question 17

For each of the following scenarios indicate which is the predictor variable and which
is the response variable.
a. A supermarket chain gathers data on the amount they spend on promotional material
(specials, coupons, etc.) and sales revenue generated each quarter.
b. Government-sponsored research investigated the relationship between number of hours
individuals spend on the Internet and age.
c. A real estate association conducted a study on home prices and economic strength for
different regions of the United States.

Question 18

Use the following to answer questions 5 - 8.
To determine whether the cash bonus paid by a company is related to annual pay, data
were gathered for 10 account executives at Johnson Financial Group who received cash
bonuses in 2007. The data, scatterplot, and summary statistics are shown below.
Estimate the linear regression model that relates the response variable (cash bonus) to
the predictor variable (annual pay).
a. Find the slope of the regression line.
b. Find the intercept of the regression line.
c. Write the equation of the linear model.

Question 19

Use the following to answer questions 5 - 8.
To determine whether the cash bonus paid by a company is related to annual pay, data
were gathered for 10 account executives at Johnson Financial Group who received cash
bonuses in 2007. The data, scatterplot, and summary statistics are shown below.
Comment on whether each of the following conditions for correlation / linear
regression is met.
a. Quantitative variable condition.
b. Linearity condition.
c. Outlier condition

Question 20

A consumer research group investigating the relationship between the price of meat
(per pound) and the fat content (grams) gathered data that produced the following
scatterplot.
a. Describe the association between the price of meat and fat content.
b. Estimate the correlation.
c. If the point in the lower left hand corner ($2.00 per pound, 6 grams of fat) is removed,would the correlation become stronger or weaker or remain the same? Explain.

Question 21

Analyze residuals.
Linear regression was used to describe the trend in world population over time.
Below is a plot of the residuals versus predicted values. What does the plot of residuals
Suggest?

A) An outlier is present in the data set.
B) The linearity condition is not satisfied.
C) A high leverage point is present in the data set.
D) The data are not normal.
E) The equal spread condition is not satisfied.

Question 22

Write and interpret a linear regression equation.

-A small independent organic food store offers a variety of specialty coffees. To
Determine whether price has an impact on sales, the managers kept track of how many
Pounds of each variety of coffee were sold last month. Based on the data and summary
Statistics shown below, the slope of the estimated regression line that relates the response
Variable (monthly sales) to the predictor variable (price per pound) is $$\begin{array} { | l | l | l | } \hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \\\hline & \$ 3.99 & 75 \\\hline & \$ 5.99 & 60 \\\hline & \$ 7.00 & 65 \\\hline & \$ 12.00 & 45 \\\hline & \$ 4.50 & 80 \\\hline & \$ 7.50 & 70 \\\hline & \$ 15.00 & 25 \\\hline & \$ 10.00 & 35 \\\hline & \$ 12.50 & 40 \\\hline & \$ 8.99 & 50 \\\hline & & \\\hline \text { Mean } & \$ 8.75 & 54.50 \\\hline \text { Standard Deviation } & \$ 3.63 & 18.33 \\\hline \text { Correlation } & \mathbf { - 0 . 9 2 7 } & \\\hline\end{array}$$

A) 95.459.
B) .858.
C) -4.681.
D) -.858.
E) -8.999.

Question 23

Analyze scatterplots and correlation coefficients.
For the scatterplot shown below, the likely correlation coefficient is

A) +0.35
B) +0.90
C) +0.77
D) -0.89
E) -1.00

Question 24

Interpret a linear regression equation and use it to make a prediction.
Data were collected on monthly sales revenues (in $1,000s) and monthly advertising
Expenditures ($100s) for a sample of drug stores. The regression line relating revenues
(Y) to advertising expenditure (X) is estimated to be yˆ = −48.3 + 9.00x . The predicted
Sales revenue for a month in which $1,000 was spent on advertising is

A) $50,000.
B) $851.70.
C) $8,951.70.
D) $41,700.
E) $90,000.

Question 25

Interpret the value of correlation coefficients and squared correlations.

-Shown below is a correlation table showing correlation coefficients between stock
Price, earnings per share (EPS) and price / earnings (P / E) ratio for a sample of 19
Publicly traded companies. Which of the following statements is false?
Correlations: Stock Price, EPS, PE $$\begin{array} { l r r } & \text { Stock Price } & \text { EPS } \\\text { EPS } & 0.875 & \\\text { PE } & 0.323 & - 0.111\end{array}$$

A) EPS is the best predictor of stock price.
B) The strongest correlation is between EPS and stock price.
C) There is a weak negative association between PE and EPS.
D) PE is the best predictor of stock price.
E) The weakest correlation is between PE and EPS.

Question 26

Interpret the value of correlation coefficients and squared correlations.

-A small independent organic food store offers a variety of specialty coffees. To
Determine whether price has an impact on sales, the managers kept track of how many
Pounds of each variety of coffee were sold last month. Based on the summary statistics
Shown below, what percent of the variability in the number of pounds of coffee sold per
Week can be explained by price? $$\begin{array} { | l | l | l | } \hline \text { Mean } & \$ 8.75 & 54.50 \\\hline \text { Standard Deviation } & \$ 3.63 & 18.33 \\\hline \text { Correlation } & \mathbf { - 0 . 9 2 7 } & \\\hline\end{array}$$

A) 95.47%
B) 100%
C) 85.9%
D) 55.6%
E) 4.68%

Question 27

Understand the relationship between the correlation and the regression line.
A company studying the productivity of their employees on a new information system
Was interested in determining if the age (X) of data entry operators influenced the number
Of completed entries made per hour (Y). The regression equation is yˆ = 14.374 − 0.145x .
If sx=14.04 and sy=2.61, then the correlation coefficient between age and productivity is

A) .779
B) -.236
C) .575
D) -.929
E) -.779

Question 28

Analyze scatterplots and correlation coefficients.
A small independent organic food store offers a variety of specialty coffees. To
Determine whether price has an impact on sales, the managers kept track of how many
Pounds of each variety of coffee were sold last month. Based on the scatterplot, the
Linear relationship between number of pounds of coffee sold per week and price is

A) strong and positive.
B) strong and negative.
C) weak and negative.
D) weak and positive.
E) nonexistent.

Question 29

Analyze scatterplots and correlation coefficients.
A consumer research group examining the relationship between the price of meat (per
Pound) and fat content (in grams) gathered data that produced the following scatterplot.
If the point in the lower left hand corner (2 grams of fat; $3.00 per pound) is removed, the
Correlation would most likely

A) remain the same.
B) become positive.
C) become weaker negative.
D) become stronger negative.
E) become zero.

Question 30

Analyze residuals.
Based on the following residual plot, which condition / assumption for linear
Regression is not satisfied?

A) Linearity.
B) Quantitative Variables.
C) Equal Spread.
D) Outlier.
E) None of the above; all conditions are satisfied.

Question 31

Interpret a linear regression equation and use it to make a prediction.
A company studying the productivity of its employees on a new information system
Was interested in determining if the age (X) of data entry operators influenced the number
Of completed entries made per hour (Y). The regression equation is yˆ = 14.374 − 0.145x .
Suppose the actual completed entries per hour for an operator who is 35 years old was 8.
The residual is

A) -1.3
B) 2.6
C) -3.5
D) 1.3
E) -2.2

Question 32

Write and interpret a linear regression equation.

-A small independent organic food store offers a variety of specialty coffees. To
Determine whether price has an impact on sales, the managers kept track of how many
Pounds of each variety of coffee were sold last month. Based on the data and summary
Statistics shown below, the intercept of the estimated regression line that relates the
Response variable (monthly sales) to the predictor variable (price per pound) is $$\begin{array} { | l | l | l | } \hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \\\hline & \$ 3.99 & 75 \\\hline & \$ 5.99 & 60 \\\hline & \$ 7.00 & 65 \\\hline & \$ 12.00 & 45 \\\hline & \$ 4.50 & 80 \\\hline & \$ 7.50 & 70 \\\hline & \$ 15.00 & 25 \\\hline & \$ 10.00 & 35 \\\hline & \$ 12.50 & 40 \\\hline & \$ 8.99 & 50 \\\hline & & \\\hline \text { Mean } & \$ 8.75 & 54.50 \\\hline \text { Standard Deviation } & \$ 3.63 & 18.33 \\\hline \text { Correlation } & - \mathbf { 0 . 9 2 7 } & \\\hline\end{array}$$

A) 95.459.
B) .858.
C) -4.684.
D) -.858.
E) -8.999.

Question 33

Interpret a linear regression equation and use it to make a prediction.
Data were collected on monthly sales revenues (in $1,000s) and monthly advertising
Expenditures ($100s) for a sample of drug stores. The regression line relating revenues
(Y) to advertising expenditure (X) is estimated to be yˆ = −48.3 + 9.00x . The correct
Interpretation of the slope is that for each additional

A) $1 spent on advertising, predicted sales revenue increases by $9,000.
B) $100 spent on advertising, predicted sales revenue increases by $9,000.
C) $100 spent on advertising, predicted sales revenue decreases by $9,000.
D) $1,000 in sales revenue, advertising expenditures decrease by $48.30.
E) $100 in sales revenue, advertising expenditures decrease by $48.30.

Question 34

Check conditions for correlation and linear regression.
A small independent organic food store offers a variety of specialty coffees. To
Determine whether price has an impact on sales, the managers kept track of how many
Pounds of each variety of coffee were sold last month. Based on the scatterplot shown
Below, which of the following statements is true?

A) The quantitative variable condition is satisfied.
B) The linearity condition is satisfied.
C) There are no obvious outliers.
D) All of the above.
E) None of the above.

Question 35

Understand the relationship between the correlation and the regression line.
Suppose the correlation, r, between two variables x and y is -0.44. What would you
Predict about a y value if the x value is 2 standard deviations above its mean?

A) It will be .88 standard deviations below its mean.
B) It will be .88 standard deviations above its mean.
C) It will be 2 standard deviations below its mean.
D) It will be .44 standard deviations below its mean.
E) It will be .44 standard deviations above its mean.

Question 36

Interpret the value of correlations coefficients and squared correlations.
Suppose the correlation, r, between two variables x and y is -0.44. What percentage of
The variability in y cannot be explained by x?

A) 19%
B) 44%
C) 81%
D) 88%
E) 12%