Deck 6: Correlation and Linear Regression

Question 1

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 1

E

Question 2

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.

Answer 2

a.Positive and strong.
b.Yes: variables are quantitative, the relationship is straight enough, and there are no
apparent outliers.
c..914 is the correlation; a value between .85 and .95 is acceptable.

Question 3

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 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

Answer 3

A

Question 4

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

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 5

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 6

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 7

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 8

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 9

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 .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 10

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 11

Use the following to answer questions
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?

Question 12

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 13

Use the following to answer questions
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 14

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 15

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 .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 16

Use the following to answer questions
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 17

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.

Question 18

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 19

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 If =2.61, then the correlation coefficient between age and productivity is

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

Question 20

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 21

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

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%

Question 23

For the following scatterplot,

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

Question 24

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.