Deck 6: Exploring Data: Relationships

Question 1

Use the following to answer Questions 19-24.
What is the slope of the regression line?

Answer 1

about

Question 2

When the units of measurement are changed, what happens to the correlation of the data?

Answer 2

The correlation does not change.

Question 3

Is it possible for the correlation for a scatterplot to change dramatically when a single point is moved?

Answer 3

It is possible to change the value from positive to negative by moving a single outlier.

Question 4

What are two variables associated with professional baseball players that are most likely negatively associated?

Question 5

Suppose the equation for a regression line has a positive slope. What type of association exists between the variables?

Question 6

Suppose the equation for a regression line is y = 18 − 3x. If y = 9, what is the predicted corresponding value for x?

Question 7

Suppose the equation for a regression line is y = 18 − 3x. If x = 4, what is the predicted corresponding value for y?

Question 8

Suppose the equation for a regression line is y = 4x + 6. If x = 5, what is the predicted corresponding value for y?

Question 9

Use the following to answer Questions 19-24.
What is the y-intercept of the regression line?

Question 10

When you are interested in the relation between smoking status and death from lung cancer, identify the response variable.

Question 11

What can you say about the slope of a regression line for variables that are negatively associated?

Question 12

Suppose the babies in a nursery are surveyed. What type of association would you expect between a child's age and the average number of hours the child sleeps in a day?

Question 13

When you are interested in the relation between the class size and course evaluation, identify the explanatory variable.

Question 14

Suppose the children of a primary school are surveyed. What type of association would you expect between their ages and their height?

Question 15

What are two variables associated with professional baseball players that are most likely positively associated?

Question 16

If all the points of a scatterplot lie on a straight line, what can you say about the correlation of the data?

Question 17

Suppose the equation for a regression line is y = 4x + 6. If y = 12, what is the predicted corresponding value for x?

Question 18

Suppose the regression line for a scatterplot passes through the points (0, 30) and
(5, 20). What type of association exists between the variables?

Question 19

Suppose the regression line for a scatterplot passes through the points (0, 10) and
(5, 20). What type of association exists between the variables?

Question 20

If there is an association between two variables, is it reasonable to presume that changes in one variable will cause changes in the other variable?

Question 21

Suppose a scatterplot shows four clusters at each corner of the plot. What can you say about the feasibility of using a least-squares regression line to describe these data?

Question 22

Use the following data to answer Questions 26 - 28.
Make a scatterplot of the data.

Question 23

If two variables are both positive, and tend to be linked so that growth of one variable tends to indicate growth in the other variable, then:

A) the variables are positively associated.
B) the variables are negatively associated.
C)
D) the variables have no association with each other.
The association of the variables cannot be determined.

Question 24

Use the following to answer Questions 19-24.
According to the regression equation, what is the expected GPA of a student who parties 30 hours a week?

Question 25

An outlier is an individual value that:

A) extends the pattern.
B) deviates from the pattern.
C) determines the strength of the relationship.
D) outlines the general form of the data.

Question 26

Use the following to answer Questions 19-24.
What is the correlation for these data?

Question 27

If two variables are negatively associated, then above-average values of one tend to accompany:

A) below-average values of the other.
B) above-average values of the other.
C) oppositely signed values of the other.
D) negatively signed values of the other.

Question 28

Can outliers significantly affect the least-squares regression line?

Question 29

Use the following to answer Questions 19-24.
If you remove the student who parties 60 hours per week from the data set, what is the correlation?

Question 30

Use the following data to answer Questions 26 - 28.
Does the data have an outlier?

Question 31

Describe the form, direction, and strength of the relationship below.

Question 32

A Little League manager keeps a record book showing the statistics for his players. The first few lines of the record book show: What are the individuals and the variables in these data?

Question 33

Ten crickets were observed under various temperatures and the number of chirps each cricket made per second was recorded. The results are shown in the table below. Make a scatterplot. Is the association between these variables positive or negative?

Question 34

If a regression line for two variables has a small positive slope, then:

A) the variables are positively associated.
B) the variables are negatively associated.
C) the association of the variables cannot be determined.
D) the variables have no association with each other.

Question 35

Below is the scatterplot for data collected on two variables. Would a least-squares regression equation be useful in describing the relationship between the variables? Why or why not?

Question 36

The least-squares regression line is the "best" line in that it minimizes a certain sum. What is this sum?

Question 37

Use the following to answer Questions 19-24.
Which student in this data set is an outlier?

Question 38

Use the following data to answer Questions 26 - 28.
What type of association exists between the variables on the scatterplot?

Question 39

Suppose that ages and hours of time slept per day are gathered from people at a mall. According to these data, young children and older adults tend to sleep more than older children and younger adults. How could you describe the resulting scatterplot of this data, where x represents ages and y represents the amount of sleep per day?

Question 40

Use the following to answer Questions 19-24.
Below are data on the age of 10 cars and the amount of money spent on auto repairs in one year. Make a scatterplot of the data.

Question 41

The least-squares regression line minimizes the sum of:

A) the squares of the shortest distance from each scatterplot point to the regression line.
B) the squares of the vertical distance from each scatterplot point to the regression line.
C) the squares of the horizontal distance from each scatterplot point to the regression line.
D) None of the above.

Question 42

If the correlation between two variables is 1, then the points of their scatterplot:

A) all lie within 1 unit of the regression line.
B) all lie within ½ unit of the regression line.
C) all lie on the regression line.
D) lie so that exactly half of the points are on each side of the regression line.

Question 43

If two variables are negatively associated, then the regression line:

A) has a negative intercept.
B) has a negative slope.
C) has negative coefficients.
D) is valid for only negative values.

Question 44

If the regression line is , which of the following must hold true?

A) The variables have a strong correlation.
B) The variables have a negative association.
C)
D) The scatterplot shows a linear trend.
All of the above.

Question 45

If the least-squares regression line is y = 3x − 5, the value y = 1 is predicted for what value of x?

A) 0
B) 1
C) 2
D) 6

Question 46

How does an outlier effect the correlation?

A) A single outlier has no effect.
B) A single outlier has minimal effect.
C) A single outlier can change the value of the correlation, but not its sign.
D) A single outlier can change the value and the sign of the correlation.

Question 47

If the correlation between two variables is −1, then the points of their scatterplot:

A) all lie within 1 unit of the regression line.
B) all lie within ½ unit of the regression line.
C) all lie on the regression line.
D) lie so that exactly half of the points are on each side of the regression line.

Question 48

If the regression line is , which of the following must hold true?

A) The variables have a weak correlation.
B) The variables have a positive association.
C)
D) The scatterplot shows a linear trend.
All of the above.

Question 49

If the correlation between x and y is 0, this means that:

A) the scatterplot has no pattern.
B) the data do not show a linear trend.
C) Both A and B are correct.
D) Neither A nor B is correct.

Question 50

A data set has . What is the standardized value of ?

A) 1
B)
C) 2
D)

Question 51

If the units of measurement change to larger units, then the correlation:

A) becomes larger.
B) becomes smaller.
C)
D) does not change.
Can either become larger or smaller.

Question 52

The intercept of the least-squares regression line is:

A) the mean of the y values.
B) the mean of the x values.
C) the mean of the y values minus the mean of the x values.
D) None of the above.

Question 53

If the least-squares regression line is then what is the residual for the point (10, 5)?

A)
B) 3
C) 8
D)

Question 54

The slope of the least-squares regression line is:

A) the correlation between the variables.
B) the same sign as the correlation between the variables.
C) the opposite of the correlation between the variables.
D) the opposite sign of the correlation between the variables.

Question 55

If the least-squares regression line is then what is the residual for the point (7, 5)?

A) 2
B) 3
C)
D)

Question 56

If the variables have a negative association, then their correlation:

A) must be less than −1.
B) must be between −1 and 0.
C) must be between 0 and 1.
D) must be greater than 1.

Question 57

When the units of measurement are changed, what will happen to the least-squares regression line?

A) The slope will change its sign.
B) The y intercept will change its sign.
C)
D) The regression line will not be changed.
The sign of the slope and y intercept will remain fixed.

Question 58

If the points of a scatterplot lie on a straight line, then the correlation:

A) must be 1.
B) must be positive.
C) must be 0.
D) must be either 1 or −1.

Question 59

Use the following scatterplot to answer Questions .
For the scatterplot shown above, what can you say about the least-squares regression line?

A) Its slope is positive.
B) It passes through the point (0,0).
C) It stops at y = 800.
D) None of the above.

Question 60

If two variables named x and y have a strong positive association, then:

A) increasing x will cause y to increase.
B) making x positive will make y positive.
C) doubling x will cause y to double.
D) changes in x do not necessarily cause changes in y.

Question 61

An airline has determined that the relationship between the number of passengers (x) on a flight and the total weight (y) (in pounds) of luggage stored in the baggage compartment can be estimated by the least-squares regression equation y = 250 + 27x. Predict the weight of luggage for a flight with 125 passengers.

A) 402 pounds
B) 3625 pounds
C) 10,125 pounds
D) 34,625 pounds

Question 62

To determine the effectiveness of group study sessions, a college instructor gathers data on hours of attendance and exam scores for students in the class. Which variable, hours of attendance or exam scores, would be the response variable for a least-squares regression equation?

A) hours of attendance
B) exam scores

Question 63

The least-squares regression equation y = 50 + 0.1x gives the yield in bushels per acre of corn when x pounds of fertilizer are applied. Predict the yield for a farmer who plans to use 320 pounds of fertilizer.

A) 82 bushels per acre
B) 16,032 bushels per acre
C) 37 bushels per acre
D) 50.32 bushels per acre

Question 64

Use the following scatterplot to answer Questions .
What conclusions can you reach if you hear 18 chirps a minute?

A) The temperature is about 87.
B) The temperature is about 90.
C) This is not a valid answer; 18 is not possible.
D) The data of the scatterplot are not valid.

Question 65

To choose advertising media, a marketing analyst studies the relationship between a consumer's income and the amount spent on restaurant dining. Which variable, consumer's income or dining expenditures, would be the response variable for a least-squares regression equation?

A) consumer's income
B) dining expenditures

Question 66

A data set has . Which of the following point is on the least-squares regression line?

A) (10,3)
B) (3,1)
C) (1,3)
D) (3,10)

Question 67

Use the following scatterplot to answer Questions .
What can you say about the correlation of the data?

A) The correlation is nearly 1.
B) The correlation is nearly −1.
C) The correlation is nearly 0.
D) The data have no correlation.

Question 68

Use the following scatterplot to answer Questions .
For the scatterplot shown above, what y value would you expect to be paired with x = 9?

A) about 500
B) about 450
C) about 400
D) It's not possible to answer this question based on the data given.

Question 69

A typing service keeps data on the number of pages (x) in a manuscript and the length of time (y) (in hours) it takes to complete the typing. The least-squares regression line for the data is given by y = 20 + 0.273x. Use this to predict the amount of hours needed to type a 40-page manuscript.

A) 810.92
B) 60.273
C) 30.92
D) 16.38

Question 70

Use the following scatterplot to answer Questions .
What can you say about the association of the variables?

A) The variables are positively correlated.
B) The variables are negatively correlated.
C) The variables are not correlated.
D) The variables are not linearly correlated.

Question 71

Suppose you are taking a survey of young children. If you measure their height and their weight, what do you expect to determine about these data?

A) There is no correlation between the data.
B) There is a positive correlation between the data.
C)
D) There is a negative correlation between the data.
There is both a negative and a positive correlation between the data.

Question 72

Use the following scatterplot to answer Questions .
What can you say about the slope of the least-squares regression line?

A) The slope is zero.
B) The slope is positive.
C) The slope is negative.
D) The slope varies.

Question 73

Use the following scatterplot to answer Questions .
What can you say about outliers in the data set?

A) There are no apparent outliers.
B) There is only one outlier.
C) There are only two outliers.
D) There are many outliers.

Question 74

Use the following scatterplot to answer Questions .
For the scatterplot shown above, what can you say about the correlation?

A) It is almost 0.
B) It is between 0 and 1.
C) It is exactly 1.
D) It is greater than 1.

Question 75

A university admissions counselor wishes to predict the performance of freshmen by considering their SAT scores. Which variable, freshman GPA or SAT score, would be the explanatory variable in a least squares regression equation?

A) freshman GPA
B) SAT score

Question 76

A data set has . Which of the following point is on the least-squares regression line?

A) (2,3)
B) (2,7)
C) (3,3)
D) (7,3)

Question 77

A bank collects data on the savings and incomes of families to predict an expected increase in certificate of deposit accounts due to a 10% increase in salaries of employees at a local company. Which variable, savings or income, would be the explanatory variable?

A) family savings
B) family income

Question 78

For professional baseball players, one would expect a negative correlation between:

A) batting average and salary.
B) years of play and salary.
C) number of home runs and salary.
D) number of errors and salary.

Question 79

Use the following scatterplot to answer Questions .
What can you say about the correlation?

A) The correlation is greater than 1.
B) The correlation is exactly 1.
C) The correlation is between 0 and 1.
D) The correlation is negative.

Question 80

While you are running on a treadmill, you would expect a positive correlation between:

A) time you spend and calories you will burn.
B)
C)
D) time you spend and your weight.
Time you spend and average running speed.
None of the above.