Deck 3: Describing Bivariate Data

Question 1

A manager of a supermarket wishes to show the relationship between the number of customers who come to the store on weekends and the total volume of sales (in dollars) during the same weekend. Which of the following graphs would likely be most useful if the manager has a sample of 52 weekends worth of data?

A) bar chart
B) pie chart
C) box and whisker plot
D) scatterplot

Answer 1

D

Question 2

The correlation coefficient r is a number that indicates the direction and the strength of the relationship between the dependent variable y and the independent variable x.

Answer 2

True

Question 3

A scatterplot can be used to depict the relationship between which kinds of variables?

A) two qualitative variables
B) two quantitative variables
C) one qualitative variable and one quantitative variable
D) three quantitative variables

Answer 3

B

Question 4

For which of the following tasks can the best-fitting regression line be used?

A) for finding the actual value of y for a given value of x
B) for predicting the value of y for a given value of x
C) for calculating the correlation coefficient
D) for calculating the covariance

Question 5

Which of the following values of the correlation coefficient r indicates a stronger correlation than 0.72?

A) 0.65
B) 0.60
C) -0.70
D) -0.75

Question 6

A perfectly straight line sloping upward would produce a covariance value of +1.

Question 7

Which of the following would NOT be considered appropriate when constructing a scatterplot?

A) labelling the x and y axes
B) labelling the graph using titles
C) connecting the data points on the graph with straight lines
D) drawing the best-fitting line on the graph

Question 8

If the correlation coefficient , then there is no linear relationship whatsoever between the dependent variable y and the independent variable x.

Question 9

Given the least squares regression line y = 3.8 - 2x, which of the following best describes the relationship between the two variables?

A) The relationship between x and y is positive.
B) The relationship between x and y is negative.
C) There is no linear relationship between x and y.
D) As x decreases, so does y.

Question 10

If all the points in a scatterplot lie on the least squares regression line, then what must the correlation coefficient r be?

A) only 1.0
B) only -1.0
C) either 1.0 or -1.0
D) only 100

Question 11

Which of the following is NOT a measure of the linear relationship between two variables?

A) the covariance
B) the correlation coefficient
C) the variance
D) the coefficient of determination

Question 12

If the correlation coefficient , then all the data points lie exactly on a straight line.

Question 13

Which of the following values would be the correlation coefficient produced by a perfectly straight line sloping downward?

A) +1
B) -1
C) +2
D) -2

Question 14

The standard deviation is a measure of the linear relationship between two quantitative variables.

Question 15

Given that 100, = 64, = 60, and n = 8, what would be the slope of the best-fitting regression line?

A) 7.5
B) 0.75
C) 0.64
D) 0.60

Question 16

Generally speaking, if two variables are unrelated, what will the covariance be?

A) a large positive number
B) a large negative number
C) a positive or negative number close to zero
D) a positive number close to 1

Question 17

Suppose that a regression line for a set of data has a y-intercept of 6.75 and a slope of 1.25. From this information, is it possible to determine the actual value of y when x = 2?

A) Yes, it is 9.25.
B) Yes, it is 8.75.
C) Yes, it is 2.25.
D) No, it is not possible.

Question 18

Given that 400, = 625, = 350, and n = 10, what is the correlation coefficient?

A) 0.875
B) 0.70
C) 0.56
D) 0.156

Question 19

A perfectly straight line sloping downward would produce a covariance value of -1.

Question 20

Generally speaking, if two quantitative variables are unrelated, the covariance will be a positive or negative number close to zero.

Question 21

Legislation Poll
A councillor was interested in determining whether people between the ages of 18 and 30 years of age would react to a piece of legislation differently than people over 30 years of age. The councillor polled a sample of 150 people from his district. The resulting data are shown in the table below:
Reaction
Refer to the Legislation Poll table. Construct a pie chart for each of the age groups.

Question 22

If the linear relationship between the dependent and independent variables is positive, the scatterplot will show the data points on the (x, y) plane moving generally from the lower left corner to the upper right corner.

Question 23

Gender Differences Narrative
Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers, as shown below:
Refer to Gender Differences Narrative. Create a side-by-side bar chart to describe these data.

Question 24

When constructing a scatterplot, the independent variable x is placed on the horizontal axis, and the dependent variable y is placed on the vertical axis.

Question 25

A perfect correlation between two variables will always produce a correlation coefficient of +1.0.

Question 26

Gender Differences Narrative
Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers, as shown below:
Refer to Gender Differences Narrative. Which of the charts created in the above three questions best depicts the difference or similarity of the responses of men and women? Give reasons for your answer.

Question 27

Students' GPA Narrative
A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's grade point average (GPA) after one year of law school. The administrator took a random sample of 15 students and computed the following summary information, where x = entrance exam score and y = GPA after one year: and .
Refer to Students' GPA Narrative. Interpret the correlation coefficient found in the previous question as to whether it could be used to predict students' GPAs after the first year. Justify your answer.

Question 28

Selling Price and Age of Home Narrative
A real estate agent is interested in knowing whether there is a relationship between the age of a house and the selling price. Listed below are the ages (in years) and selling prices (in $1000s) of a sample of six houses the agent has sold in the past year:
Refer to Selling Price and Age of Home Narrative. Based on the plot in the previous question, does there appear to be a relationship between the age of a house and selling price?

Question 29

The scatterplot is a graph that is used to represent the relationship between two quantitative variables.

Question 30

The best-fitting line relating the dependent variable y to the independent variable x, often called the regression or least-squares line, is found by minimizing the sum of the squared differences between the data points and the line itself.

Question 31

Legislation Poll
A councillor was interested in determining whether people between the ages of 18 and 30 years of age would react to a piece of legislation differently than people over 30 years of age. The councillor polled a sample of 150 people from his district. The resulting data are shown in the table below:
Reaction
Refer to the Legislation Poll table. Construct a side-by-side bar chart.

Question 32

Legislation Poll
A councillor was interested in determining whether people between the ages of 18 and 30 years of age would react to a piece of legislation differently than people over 30 years of age. The councillor polled a sample of 150 people from his district. The resulting data are shown in the table below:
Reaction
Refer to the Legislation Poll table. Which of the two types of presentations in the previous two questions is more easily understood?

Question 33

A scatterplot is particularly useful in determining if the relationship between the independent and dependent variables is not linear.

Question 34

Selling Price and Age of Home Narrative
A real estate agent is interested in knowing whether there is a relationship between the age of a house and the selling price. Listed below are the ages (in years) and selling prices (in $1000s) of a sample of six houses the agent has sold in the past year:
Consider the following set of bivariate data:
a. Plot the data on a scatterplot.
b. Based on the plot in (a), are there any data points that seem unusual (i.e., are there any outliers)? If so, which one or ones?
c. Ignoring any observations you have considered to be unusual, what can be said about the relationship between the variables x and y?

Question 35

If the correlation coefficient between the independent variable x and the dependent variable y is 0.87, then the best-fitting line would have a slope equal to 0.87.

Question 36

Students' GPA Narrative
A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's grade point average (GPA) after one year of law school. The administrator took a random sample of 15 students and computed the following summary information, where x = entrance exam score and y = GPA after one year: and .
Refer to Students' GPA Narrative. Find the correlation between the entrance exam score and the grade point average after one year of law school.

Question 37

Gender Differences Narrative
Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers, as shown below:
Refer to Gender Differences Narrative. Create two pie charts (one for men and one for women) to describe these data.

Question 38

Gender Differences Narrative
Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers, as shown below:
Refer to Selling Price and Age of Home Narrative. Plot the data on a scatterplot.

Question 39

If two variables have a correlation coefficient equal to 0.005, this means that there is a strong relationship between the two variables.

Question 40

Gender Differences Narrative
Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers, as shown below:
Refer to Gender Differences Narrative. Create a stacked bar chart to describe these data.

Question 41

Soft Drink Sales Narrative
A soft drink distributor was interested in examining the relationship between the number of ads (x) for his product during prime time on a local television station and the number of sales per week (y) in 1000s of cases. She compiled the figures for 20 weeks and computed the following summary information: n = 20, and .
Refer to Soft Drink Sales Narrative. If the soft drink distributor ran 21 TV ads per week for her product, what would you predict her sales to be?

Question 42

Meet Your Match Media Narrative
The Executive Board of a popular online dating website, called Meet Your Match, wanted to know if there was a relationship between the age of a client and the number of persons they made contact with through the site. To find out, a random sample of 50 users from each of the 6 delineated age groups was drawn from its data base of active participants. The users were then surveyed as to how many persons had responded to the introduction email during the previous 3-month period. The average number of initial responses for each of the age groups was then recorded and organized into the following table.
Refer to Meet Your Match Media Narrative. What are the two primary variables of interest in this experiment? Are they qualitative or quantitative?

Question 43

Gasoline Prices and Fuel Efficiency Narrative.
When the price of gasoline gets high, consumers become very concerned about the gas mileage obtained by their cars. One consumer was interested in the relationship between car engine size (number of cylinders) and gas mileage (miles/gallon). The consumer took a random sample of 7 cars and recorded the following information:
n = 7, ?x_i = 24.7, ?y_i = 177, ?x_iy_i = 600.7, s_x = 1.2406,
and
s_y=4.3861
Refer to Gasoline Prices and Fuel Efficiency Narrative. Find the best-fitting line relating car engine size and fuel efficiency.

Question 44

Weekly Amount Spent on Groceries Narrative
The number of household members, x, and the amount spent on groceries per week, y, rounded to the nearest dollar, are measured for eight households in Lakehead area. The data are shown below:
Refer to Weekly Amount Spent on Groceries Narrative. Find the best-fitting regression line for these data.

Question 45

Meet Your Match Media Narrative
The Executive Board of a popular online dating website, called Meet Your Match, wanted to know if there was a relationship between the age of a client and the number of persons they made contact with through the site. To find out, a random sample of 50 users from each of the 6 delineated age groups was drawn from its data base of active participants. The users were then surveyed as to how many persons had responded to the introduction email during the previous 3-month period. The average number of initial responses for each of the age groups was then recorded and organized into the following table.
Refer to Meet Your Match Media Narrative. Of all the graphical techniques available for displaying data, which would be the most useful to determine if any kind of relationship existed between the two variables? Justify your answer.

Question 46

Weekly Amount Spent on Groceries Narrative
The number of household members, x, and the amount spent on groceries per week, y, rounded to the nearest dollar, are measured for eight households in Lakehead area. The data are shown below:
Refer to Weekly Amount Spent on Groceries Narrative. What would you estimate a household of seven to spend on groceries per week? Should you use the fitted line to estimate this amount? Why or why not?

Question 47

Soft Drink Sales Narrative
A soft drink distributor was interested in examining the relationship between the number of ads (x) for his product during prime time on a local television station and the number of sales per week (y) in 1000s of cases. She compiled the figures for 20 weeks and computed the following summary information: n = 20, and .
Refer to Soft Drink Sales Narrative. Find the correlation coefficient for the number of ads during prime time and weekly sales.

Question 48

Weekly Amount Spent on Groceries Narrative
The number of household members, x, and the amount spent on groceries per week, y, rounded to the nearest dollar, are measured for eight households in Lakehead area. The data are shown below:
Refer to Weekly Amount Spent on Groceries Narrative. Draw a scatter plot of these eight data points

Question 49

Meet Your Match Media Narrative
The Executive Board of a popular online dating website, called Meet Your Match, wanted to know if there was a relationship between the age of a client and the number of persons they made contact with through the site. To find out, a random sample of 50 users from each of the 6 delineated age groups was drawn from its data base of active participants. The users were then surveyed as to how many persons had responded to the introduction email during the previous 3-month period. The average number of initial responses for each of the age groups was then recorded and organized into the following table.
Refer to Meet Your Match Media Narrative. What are the experimental units?

Question 50

Gasoline Prices and Fuel Efficiency Narrative.
When the price of gasoline gets high, consumers become very concerned about the gas mileage obtained by their cars. One consumer was interested in the relationship between car engine size (number of cylinders) and gas mileage (miles/gallon). The consumer took a random sample of 7 cars and recorded the following information:
n = 7, ?x_i = 24.7, ?y_i = 177, ?x_iy_i = 600.7, s_x = 1.2406,
and
s_y=4.3861
Refer to Gasoline Prices and Fuel Efficiency Narrative. What fuel efficiency would you predict for a car with a 6-cylinder engine?

Question 51

Meet Your Match Media Narrative
The Executive Board of a popular online dating website, called Meet Your Match, wanted to know if there was a relationship between the age of a client and the number of persons they made contact with through the site. To find out, a random sample of 50 users from each of the 6 delineated age groups was drawn from its data base of active participants. The users were then surveyed as to how many persons had responded to the introduction email during the previous 3-month period. The average number of initial responses for each of the age groups was then recorded and organized into the following table.
Refer to Meet Your Match Media Narrative. What is the sample size?

Question 52

Gasoline Prices and Fuel Efficiency Narrative.
When the price of gasoline gets high, consumers become very concerned about the gas mileage obtained by their cars. One consumer was interested in the relationship between car engine size (number of cylinders) and gas mileage (miles/gallon). The consumer took a random sample of 7 cars and recorded the following information:
n = 7, ?x_i = 24.7, ?y_i = 177, ?x_iy_i = 600.7, s_x = 1.2406,
and
s_y=4.3861
Refer to Gasoline Prices and Fuel Efficiency Narrative. Find the correlation between engine size and fuel efficiency.

Question 53

Gasoline Prices and Fuel Efficiency Narrative.
When the price of gasoline gets high, consumers become very concerned about the gas mileage obtained by their cars. One consumer was interested in the relationship between car engine size (number of cylinders) and gas mileage (miles/gallon). The consumer took a random sample of 7 cars and recorded the following information:
n = 7, ?x_i = 24.7, ?y_i = 177, ?x_iy_i = 600.7, s_x = 1.2406,
and
s_y=4.3861
Refer to Gasoline Prices and Fuel Efficiency Narrative. Would you expect the correlation between engine size and fuel efficiency to be positive or negative?

Question 54

Students' GPA Narrative
A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's grade point average (GPA) after one year of law school. The administrator took a random sample of 15 students and computed the following summary information, where x = entrance exam score and y = GPA after one year: and .
Refer to Students' GPA Narrative. If a student scored 91 on the entrance exam, what would you predict the student's grade point average to be after one year of law school?

Question 55

Soft Drink Sales Narrative
A soft drink distributor was interested in examining the relationship between the number of ads (x) for his product during prime time on a local television station and the number of sales per week (y) in 1000s of cases. She compiled the figures for 20 weeks and computed the following summary information: n = 20, and .
Refer to Soft Drink Sales Narrative. Find the best-fitting line relating the number of ads during prime time and weekly sales.

Question 56

Weekly Amount Spent on Groceries Narrative
The number of household members, x, and the amount spent on groceries per week, y, rounded to the nearest dollar, are measured for eight households in Lakehead area. The data are shown below:
Refer to Weekly Amount Spent on Groceries Narrative. Plot the points and the best-fitting line on the same graph.

Question 57

Students' GPA Narrative
A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's grade point average (GPA) after one year of law school. The administrator took a random sample of 15 students and computed the following summary information, where x = entrance exam score and y = GPA after one year: and .
Refer to Students' GPA Narrative. Find the best-fitting line relating grade point average after one year of law school and score on the entrance exam.