Deck 6: Scatterplots, Association, and Correlation

Question 1

Consider the following to answer the question(s) below:
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.
If the point in the lower left hand corner ($2.00 per kilogram, 6 grams of fat) were removed, the correlation would most likely

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

Answer 1

B

Question 2

Based on the scatterplots shown below, describe the association between x and y.
a. b.

Answer 2

a. The association between x and y is positive and moderately strong.
b. There is no apparent relationship between x and y.

Question 3

Based on the scatterplots shown below, describe the association between x and y.
a. b.

Answer 3

a. There is no apparent relationship between x and y.
b. There is a very strong positive linear relationship between x and y.

Question 4

A supermarket chain gathers data on the amount they spend on promotional material (specials, 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) not possible to be determined

Question 5

Consider the following to answer the question(s) below:
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.
Which best describes the association between the price of meat and fat content?

A) Negative, moderately strong
B) Negative, weak
C) Positive, strong
D) Positive, weak
E) No apparent association

Question 6

A consumer research group investigating the relationship between the price of meat (per kilogram) 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 kilogram, 6 grams of fat) is removed, would the correlation become stronger, weaker, or remain the same? Explain.

Question 7

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

Question 8

Consider the following to answer the question(s) below:
The following scatterplot shows monthly sales figures (in units) and the number of months of experience on the job for a sample of 18 salespeople.
The association between monthly sales and number of months 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 9

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. 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 10

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." Which of the following is true regarding this statement?

A) The correlation between the use of online bill paying and gender is negative.
B) The correlation between the use of online bill paying and gender is positive.
C) 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.
D) More males will bank online compared with females.
E) More females will bank online compared with males.

Question 11

The following scatterplot shows a relationship between x and y that results in a correlation 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.

Question 12

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 13

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 14

Government sponsored research investigated the relationship between the number of hours individuals spend on the Internet and age. Which of the following statements is true?

A) Age is the predictor variable and number of hours spent on the Internet is the response variable.
B) Government is the predictor variable and the number of hours spent on the Internet is the response variable.
C) Age is the response variable and the number of hours spent on the Internet is the predictor variable.
D) Age is the predictor variable and government sponsored research is the response variable.
E) It is not possible to determine the predictor variable.

Question 15

The following scatterplot shows monthly sales figures (in units) and number of months of experience on the job for a sample of 18 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 16

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 17

A study examined consumption levels of oil and carbon dioxide emissions for a sample of counties. The response variable in this study is

A) oil
B) oil consumption
C) carbon dioxide emissions
D) countries
E) oil and carbon dioxide

Question 18

The following scatterplot shows Internet Usage and PC adoption (per 100 inhabitants) for a sample of 15 countries. a. Describe the association between Internet usage and PC adoption.
b. Do these data satisfy the conditions for computing a correlation coefficient? Explain.
c. Estimate the correlation.

Question 19

Consider the following to answer the question(s) below:
The following scatterplot shows monthly sales figures (in units) and the number of months of experience on the job for a sample of 18 salespeople.
The correlation between monthly sales and number of months of experience is most likely

A) -0.235
B) 0
C) 0.180
D) -0.914
E) 0.914

Question 20

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 the 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 Canada.

Question 21

Which of the following statements is correct?

A) A scatter plot showing two variables with a positive linear relationship will have all points on a straight line.
B) The stronger the linear relationship between two variables, the closer the correlation coefficient will be to +1.0.
C) Two variables that are uncorrelated with one another may still be related in a nonlinear manner.
D) A curvilinear relationship will always have a correlation coefficient of zero.
E) All of the above are correct.

Question 22

The University recently sampled five full time students who work off campus in order to look at their GPA and their work schedules. The standard deviation for GPA is 0.91 and the standard deviation for hours worked is 6.78. These sample data are shown as follows: Given these data the sample correlation is

A) -0.4862
B) -0.3890
C) -0.4214
D) -0.3371
E) -0.3578

Question 23

If a pair of variables have a curvilinear relationship, which of the following is true?

A) The correlation coefficient will not be able to indicate the relationship is curved.
B) The correlation coefficient will be zero.
C) The correlation coefficient will indicate that the relationship is curved.
D) The scatter plot will not be able to indicate the relationship is curved.
E) Outliers cause the curve.

Question 24

Consider the following sample data. The standard deviations from the data are 3.67 for Y, and 45.28 for X. These sample data are shown as follows: Given this data, the sample correlation is approximately

A) 0.6770
B) 0.5416
C) 0.1565
D) 0.3585
E) 0.1956

Question 25

Shown below is a correlation table showing correlation coefficients between stock price, earnings per share (EPS), and the price/earnings (P/E) ratio for a sample of 19 publicly traded companies. Which of the following statements is false?

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 P/E and EPS.
D) PE is the best predictor of stock price.
E) The weakest correlation is between P/E and EPS.

Question 26

A perfect correlation between two variables will always produce which of the following?

A) a correlation coefficient of -1.0
B) a scatter plot with a pattern running from lower left to upper right
C) a correlation coefficient of 1.0
D) a scatter plot where all points lie on a single straight line
E) a scatter plot with a pattern running from upper left to lower right

Question 27

In analyzing the relationship between two variables, a scatter plot can be used to detect which of the following?

A) a positive linear relationship
B) a negative linear relationship
C) a curvilinear relationship
D) the presence of a potential outlier
E) all of the above

Question 28

A study was done in which the daily temperature and the number of traffic accidents within the city were recorded. The standard deviations for the samples are 13.13 for temperature and 2.55 for accidents. These sample data are shown as follows: Given these data, the sample correlation is approximately

A) 0.5453
B) -0.1162
C) 0.3883
D) -0.5453
E) -0.3883

Question 29

Assume that a medical research study found a correlation of -0.73 between regular use of sunscreen and the skin cancer rate. This could be interpreted to mean that

A) the greater the regular use of sunscreen, the lower the person's chances of getting skin cancer.
B) skin cancer is caused by not using sunscreen regularly.
C) the greater the regular use of sunscreen, the higher the person's chances of getting skin cancer.
D) skin cancer can be prevented by regular use of sunscreen.
E) the lower the regular use of sunscreen, the lower the person's chances of getting skin cancer.

Question 30

In a university statistics course a correlation of -0.8 was found between number of classes missed and course grade. This can be interpreted to mean that

A) The more classes missed, the lower the course grade.
B) A lower course grade is caused by missing more classes.
C) The correlation is strong and positive.
D) A higher grade can be achieved by missing fewer classes.
E) The more classes missed, the higher the course grade.

Question 31

If the correlation between two variables is determined to be 0.70, which of the following is known to be true?

A) The relationship between them is positive.
B) The relationship between the two is negative.
C) The scatter diagram for the two variables will be upward sloping from left to right.
D) The scatter diagram for the two variables will be downwards sloping from left to right.
E) A and C

Question 32

The correlation associated with the following scatterplot is

A) 1.00
B) -1.00
C) 0.50
D) -0.50
E) 0.00