Deck 12: Linear Regression and Correlation

Question 1

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected:
What is the dependent variable?

A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the choices are correct
E) None of the choices are correct

Answer 1

Amount of sales

Question 2

In the regression equation, Y' = a + bX, what does the letter "a" represent?

A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) None of these statements are correct

Answer 2

A

Question 3

i. If we are studying the relationship between high school performance and college performance, and want to predict college performance, high school performance is the independent variable.
ii. A financial advisor is interested in predicting bond yield based on bond term, i.e., one year, two years, etc. The dependent variable is bond yield.
Iii) The variable used to predict the value of another is called the independent variable.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Answer 3

(i), (ii) and (iii) are all correct statements

Question 4

A scatter diagram is a chart

A) In which the dependent variable is scaled along the vertical axis.
B) In which the independent variable is scaled along the horizontal axis.
C) That portrays the relationship between two variables.
D) All of the above.

Question 5

i. If we are studying the relationship between high school performance and college performance, and want to predict college performance, high school performance is the independent variable.
Ii) An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.
Iii) The variable used to predict the value of another is called the dependent variable.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 6

Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. A scatter diagram of the collected information is shown below. Looking at this scatter diagram you determine:

A) There is clearly no relationship between the number of sales contacts made and the sales earned.
B) There is a moderate but inverse relationship between the two variables
C) There is a moderate and direct relationship between the two variables
D) The Sales ($000s) is the independent variable
E) C & D are true

Question 7

i. The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.
ii. When a regression line has a zero slope, indicating a lack of a relationship, the line is vertical to the x-axis.
Iii) In regression analysis, the predicted value of Y' rarely agrees exactly with the actual Y value, i.e., we expect some prediction error.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 8

i. The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis.
ii. In order to visualize the form of the regression equation, we can draw a scatter diagram.
Iii) When a regression line has a zero slope, indicating a lack of a relationship, the line is horizontal to the x-axis.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 9

What is the independent variable?

A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the choices are correct
E) None of the choices are correct

Question 10

Given the scatter diagram below, that shows the number of workdays absent per year based on the age of the employees, which of the following statements are true?

A) There is clearly no relationship whatsoever between an employee's age and the number of workday absences that they take.
B) There is a single but strong outlier in this data set.
C) There appears to be an inverse relationship between the two variables
D) A & B are true
E) B & C are true

Question 11

i. In order to visualize the form of the regression equation, we can draw a scatter diagram.
ii. The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.
Iii) In regression analysis, the predicted value of Y' rarely agrees exactly with the actual Y value, i.e., we expect some prediction error.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 12

Given the scatter diagram below, that shows the number of workdays absent per year based on the age of the employees, which of the following statements are true?

A) There is clearly no relationship whatsoever between an employee's age and the number of workday absences that they take.
B) There is a single but strong outlier in this data set.
C) In analyzing this data, you may wish to remove the one point that doesn't "fit" with all the others before continuing your analysis.
D) A & B are true
E) B & C are true

Question 13

i. If we are studying the relationship between high school performance and college performance, and want to predict college performance, high school performance is the dependent variable.
Ii) A financial advisor is interested in predicting bond yield based on bond term, i.e., one year, two years, etc. The dependent variable is bond term.
Iii) The variable used to predict the value of another is called the dependent variable.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 14

In the equation Y' = a + bX, what is Y'?

A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X = 0
E) None of these statements are correct

Question 15

Suppose the least squares regression equation is Y' = 1202 + 1,133X. When X = 3, what does Y' equal?

A) 5,734
B) 8,000
C) 4,601
D) 4,050
E) None of these statements are correct

Question 16

i. In order to visualize the form of the regression equation, we can draw a scatter diagram.
ii. When a regression line has a zero slope, indicating a lack of a relationship, the line is vertical to the x-axis.
Iii) In regression analysis, the predicted value of Y' rarely agrees exactly with the actual Y value, i.e., we expect some prediction error.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 17

i. A scatter diagram is a chart that portrays the relationship between two variables.
ii. If a scatter diagram shows very little scatter about a straight line drawn through the plots, it indicates a rather weak relationship.
Iii) A scatter diagram may be put together using excel or megastat.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 18

What is the variable used to predict the value of another called?

A) Independent
B) Dependent
C) Correlation
D) Determination
E) None of these statements are correct

Question 19

In the regression equation, Y' = a + bX, what does the letter "b" represent?

A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) Value of Y when X = 0
E) None of these statements are correct

Question 20

What is the chart called when the paired data (the dependent and independent variables) are plotted?

A) Scatter diagram
B) Bar
C) Pie
D) Linear regression
E) None of these statements are correct

Question 21

Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. The Excel printout is shown below.
This model predicts that with 25 sales contacts, sales will be:

A) $49 576
B) $42 022
C) $190 843
D) $19 429
E) $16 605

Question 22

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below:
From this printout you determine:

A) The employee age is the dependent variable
B) The employee age is the independent variable
C) The older the employee the more days they are absent from work
D) The intercept of 23 indicates the most days absent
E) B & C are true

Question 23

The partial megastat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis
Is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports.
Refer to the printout above. Predict the annual attendance (000) for a team with 100 wins

A) 2,820.49
B) 3,222.61
C) 2,903.01
D) 3,695.06
E) 8,279.78

Question 24

Given the following five points: (-2,0), (-1,0), (0,1), (1,1), and (2,3). What is the Y intercept?

A) 0.0
B) 0.7
C) 1.0
D) 1.5
E) None of the choices are correct

Question 25

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below:
From this printout you determine:

A) When tested at the 2% level of significance, there is no relationship between an employee's age and the number of days of work absences
B) For each additional year of age, we can expect the number of days of absence to increase by 0.45 days
C) Almost 53% of the variation in the number of absent days can be explained by the variation in the employees ages
D) A & B are true
E) A & C are true

Question 26

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below:
From this printout you determine:

A) The employee age is the dependent variable
B) The employee age is the independent variable
C) The regression equation is Y = 23.57 - 0.45x
D) The regression equation is Y = 23.57 x -0.45
E) B & C are true

Question 27

Assume the least squares equation is Y' = 10 + 20X. What does the value of 10 in the equation indicate?

A) Y intercept
B) For each unit increased in Y, X increases by 10
C) For each unit increased in X, Y increases by 10
D) None of these statements are correct

Question 28

In the least squares equation, Y' = 10 + 20X the value of 20 indicates

A) the Y intercept.
B) for each unit increased in X, Y increases by 20.
C) for each unit increased in Y, X increases by 20.
D) None of these statements are correct.

Question 29

i. The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis.
ii. In order to visualize the form of the regression equation, we can draw a scatter diagram.
Iii) The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 30

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized
Below:
From this printout you determine:

A) The y-intercept of 23 makes no sense
B) For each additional year of age, we can expect the number of days of absence to increase by 0.45 days
C) For each additional year of age, we can expect the number of days of absence to decrease by 0.45 days
D) A & B are true
E) A & C are true

Question 31

i. The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis.
ii. In order to visualize the form of the regression equation, we can draw a scatter diagram.
Iii) A regression equation may be determined using a mathematical method called the least squares principle.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 32

The partial megastat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports
Refer to the printout above. The regression equation is:

A) $\hat{y}$ = 2,049 + 68.8291x
B) $\hat{y}$ = 82.5157 + 28.2049x
C) $\hat{y}$ = 28.2049 + 7.5888x
D) $\hat{y}$ = 82.5157 + 7.5888x
E) $\hat{y}$ = 7.5888 + 28.2049x

Question 33

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below:
From this printout you determine:

A) The y-intercept of 23 makes no sense
B) The employee age is the independent variable
C) The regression equation is Y = 23.57 - 0.45x
D) B & C are true
E) All of the choices are true

Question 34

i. The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis.
ii. In order to visualize the form of the regression equation, we can draw a scatter diagram.
Iii) The equation for a straight line going through the plots on a scatter diagram is called a regression
Equation. It is alternately called an estimating equation and a predicting equation.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 35

Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. The Excel printout is shown below.
From this printout you determine:

A) There is a very weak relationship between the # of contacts and the sales $
B) There is a very strong relationship between the # of contacts and the sales $
C) The regression equation is y = 1.98 x +7.55
D) The regression equation is y = -7.55 x +1.98
E) B & C are true

Question 36

i. In order to visualize the form of the regression equation, we can draw a scatter diagram.
ii. In regression analysis, the predicted value of Y' rarely agrees exactly with the actual Y value, i.e., we expect some prediction error.
Iii) The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 37

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below:
From this printout you determine:

A) The employee age is the dependent variable
B) The employee age is the independent variable
C) The regression equation is Y = 23.57 - 0.45x
D) The regression equation is Y = 23.57 x -0.45
E) B & C are true

Question 38

i. The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis.
ii. In order to visualize the form of the regression equation, we can draw a scatter diagram.
Iii) A line found using the least squares principle is the best-fitting line because the sum of the squares of the vertical deviations between the actual and estimated values is minimized.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 39

Given the following five points: (-2,0), (-1,0), (0,1), (1,1), and (2,3). What is the slope of the line?

A) 0.0
B) 0.5
C) 0.6
D) 0.7
E) None of the choices are correct

Question 40

i. The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis.
ii. In order to visualize the form of the regression equation, we can draw a scatter diagram.
Iii) When a regression line has a zero slope, indicating a lack of a relationship, the line is horizontal to the x-axis.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 41

The partial megastat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports.
Refer to the printout above. Predict the number of wins for a team with PAYROLL = 25(million) (nearest whole number)

A) 10
B) 69
C) 79
D) 74
E) 64

Question 42

i. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
ii. Coefficients of -0.91 and +0.91 have equal strength.
Iii) If the coefficient of correlation is 0.68, the coefficient of determination is 0.4624.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 43

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected:
The slope in this instance indicates:

A) For each additional contact made, the salesperson can anticipate an additional $2195 in sales
B) For each additional contact made, the salesperson can anticipate an additional $2.19 in sales
C) For each additional contact made, the salesperson can anticipate an additional $12,201 in sales
D) For each additional contact made, the salesperson can anticipate a drop of $12,201 in sales
E) For each additional sale made, the salesperson can anticipate an additional 2 contacts are needed

Question 44

i. The strength of the correlation between two variables depends on the sign of the coefficient of correlation.
Ii) A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
Iii) Coefficients of -0.91 and +0.91 have equal strength.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 45

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Partial excel results are
Summarized below from two different samples:
Given this information alone, would you decide to continue with the regression analysis for sample #1 or #2 or both?

A) Continue with both samples, because the sample sizes are over 15
B) Continue with sample #1 because the multiple r value is larger than that of sample #2
C) Continue with sample #2 because the multiple r value is larger than that of sample #1
D) Don't continue with either sample, because the standard error values are more than 2
E) Don't continue with either sample, because the sample sizes are too small to be of use

Question 46

We have collected price per share and dividend information from a sample of 30 companies.
The slope in this instance indicates:

A) For each additional dollar in stock price, we can anticipate an additional $2.73 in dividend
B) For each additional dollar in stock price, we can anticipate an additional $3.68 in dividend
C) For each additional dollar in stock price, we can anticipate an additional $0.27 in dividend
D) For each additional dollar in dividend, we can anticipate an additional $2.71 in stock price
E) For each additional dollar in dividend, we can anticipate a drop of $3.68 in stock price

Question 47

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected:
What is the Y-intercept of the linear equation?

A) -12.201
B) 2.1946
C) -2.1946
D) 12.201
E) None of the choices are correct

Question 48

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected:
What is the slope of the linear equation?

A) -12.201
B) 12.201
C) 2.1946
D) -2.1946
E) None of the choices are correct

Question 49

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected:
What is the regression equation?

A) Y' = 2.1946 - 12.201X
B) Y' = -12.201X + 2.1946X
C) Y' = 12.201 + 2.1946X
D) Y' = 2.1946 + 12.201X
E) None of the choices are correct

Question 50

Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. The Excel printout is shown below.
The slope in this instance indicates:

A) For each additional contact made, the salesperson can anticipate an additional $1983 in sales
B) For each additional contact made, the salesperson can anticipate an additional $1.98 in sales
C) For each additional contact made, the salesperson can anticipate an additional $7,554 in sales
D) For each additional contact made, the salesperson can anticipate a drop of $7,554 in sales
E) For each additional sale made, the salesperson can anticipate an additional 2 contacts are needed

Question 51

i. The purpose of correlation analysis is to find how strong the relationship is between two variables.
ii. A correlation coefficient of -1 or +1 indicates perfect correlation.
Iii) The standard error of estimate measures the accuracy of our prediction.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 52

i. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
Ii) The coefficient of determination is the proportion of the total variation in the dependent variable Y
That is explained or accounted for by its relationship with the independent variable X.
iii. If the coefficient of correlation is -0.90, the coefficient of determination is -0.81.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 53

i. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
Ii) A coefficient of correlation of -0.96 indicates a very weak negative correlation.
iii. The coefficient of determination can only be positive.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 54

i. The strength of the correlation between two variables depends on the sign of the coefficient of correlation.
Ii) A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
Iii) The coefficient of determination is found by taking the square root of the coefficient of correlation.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) is a correct statement but not (i) or (iii).
E) All statements are false

Question 55

i. The purpose of correlation analysis is to find how strong the relationship is between two variables.
ii. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
Iii) The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 56

i. The purpose of correlation analysis is to find how strong the relationship is between two variables.
ii. A coefficient of correlation of -0.96 indicates a very weak negative correlation.
iii. The standard error of estimate measures the accuracy of our prediction.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 57

We have collected price per share and dividend information from a sample of 30 companies. Using the Megastat printout, determine the regression equation that predicts the dividend from the stock's selling price.

A) Y = 0.27 +3.68x
B) Y = 0.27x + 3.68
C) Y = -3.68 + 0.27x
D) Y = -0.27x - 3.68
E) None of the choices are correct.

Question 58

i. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
ii. If the coefficient of correlation is 0.68, the coefficient of determination is 0.4624.
iii. The standard error of estimate measures the accuracy of our prediction.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 59

Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. The Excel printout is shown below.
The y-intercept in this instance suggests:

A) For each additional contact made, the salesperson can anticipate an additional $193 in sales
B) For each additional contact made, the salesperson can anticipate a drop of $1983 in sales
C) When no contacts are made, the salesperson can anticipate sales of $7554
D) When no contacts are made, the salesperson can anticipate sales of $1983
E)When no contacts are made, the salesperson can anticipate negative sales - therefore the regression model doesn't make sense for no contacts

Question 60

We have collected price per share and dividend information from a sample of 30 companies. The y-intercept in this instance suggests:

A) For each additional dollar in stock price, we can anticipate an additional $2.73 in dividend
B) For each additional dollar in stock price, we can anticipate a drop of $2.41 in dividend
C) When the stock price is zero, we can anticipate a dividend of $0.27. This value, however, makes no sense
D) When the stock price is zero, we can anticipate a dividend of $-3.68. This value, however, makes no sense
E) When the dividends are zero, we can anticipate a negative share price

Question 61

i. The coefficient of determination is the proportion of the total variation in the dependent variable Y that is explained or accounted for by its relationship with the independent variable X.
Ii) The coefficient of determination is found by taking the square root of the coefficient of correlation.
iii. The standard error of estimate measures the accuracy of our prediction.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 62

i. If the value of r is -0.96, what does this indicate about the dependent variable as the independent variable increases?
Ii) What is the value of the correlation coefficient if there is perfect correlation?
Iii) If the dependent variable is measured in dollars, in what units is the standard error of estimate measured?

A) it increases; zero, dollars squared
B) it decreases; +/- 1.0, dollars squared
C) it increases; 1.0, dollars ($)
D) it decreases; +/- 1.0; dollars ($)
E) it decreases; zero; dollars

Question 63

The partial megastat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis
Is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports.
Refer to the printout above. How many independent variables?

A) 1
B) 2
C) 9
D) 10
E) 11

Question 64

What does the coefficient of determination equal if r = 0.89?

A) 0.94
B) 0.89
C) 0.79
D) 0.06
E) None of these statements are correct

Question 65

What is the range of values for a coefficient of correlation?

A) 0 to +1.0
B) -3 to +3 inclusive
C) -1.0 to +1.0 inclusive
D) Unlimited range
E) None of these statements are correct

Question 66

i. If there is absolutely no relationship between two variables, what will Pearson's r equal? ii. If the coefficient of correlation is 0.80, what is the coefficient of determination?
Iii) If the coefficient of determination is 0.81, what is the coefficient of correlation?

A) zero (0), 0.64, 0.9 or -0.9
B) zero (0), 0.64, 0.09
C) one (1), 0.64, 0.6561
D) one (1), 0.64, 0.9 or -0.9
E) zero (0), 0.8944, 0.6561

Question 67

i. The coefficient of determination can only be positive.
ii. If the coefficient of correlation is 0.68, the coefficient of determination is 0.4624.
iii. The standard error of estimate measures the accuracy of our prediction.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 68

i. If there is absolutely no relationship between two variables, what will Pearson's r equal? ii. If the value of r is -0.96, what does this indicate about the dependent variable as the independent variable increases?
Iii) What is the value of the correlation coefficient if there is perfect correlation?

A) one (1); decreases; zero (0)
B) one (1); increases; zero (0)
C) zero (0); decreases; +/- 1.0
D) zero (0); increases; +/- 1.0
E) +/- 1.0; nothing; +/- 1.0

Question 69

i. Correlation analysis is a group of statistical techniques used to measure the strength of the relationship (correlation) between two variables.
Ii) A correlation coefficient of -1 or +1 indicates perfect correlation.
Iii) The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 70

If the correlation between two variables is close to one, the association is

A) strong.
B) moderate.
C) weak.
D) none.

Question 71

i. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
Ii) A coefficient of correlation of -0.96 indicates a very weak negative correlation.
Iii) If the coefficient of correlation is 0.68, the coefficient of determination is 0.4624.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 72

i. Perfect correlation means that the scatter diagram will appear as a straight line ii. If the coefficient of correlation is 0.80, the coefficient of determination is 0.64.
iii. The coefficient of determination can assume values between 0% and 100%

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 73

Use the scatter diagrams to verify which statements are correct:
Chart A

Chart B

Chart C

A) The variables in Chart A have a strong positive correlation
B) The variables in Chart C have a strong positive correlation
C) The variables in Chart B have a negative correlation
D) Charts A & B have no obvious outliers
E) None of the choices are correct

Question 74

i. The coefficient of correlation is a measure of the strength of relationship between two variables.
ii. The coefficient of determination can only be positive.
Iii) The standard error of estimate measures the accuracy of our prediction.

A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Question 75

i. If the coefficient of correlation is 0.80, what is the coefficient of determination? ii. What is a measure of the scatter of observed values around the regression line called?
Iii) If the correlation between sales and advertising is +0.6, what percent of the variation in sales can be attributed to advertising?

A) 0.4; standard deviation; 0.3
B) 0.64; standard error of the estimate; 36%
C) 0.64; standard error of the estimate; 60%
D) 0.08; variation; 36%
E) 0.4; standard error of the estimate, 60%

Question 76

i. If the coefficient of correlation is 0.70, what is the coefficient of determination? ii. If the value of r is -0.88, what does this indicate about the dependent variable as the independent variable increases?
Iii) If the dependent variable is measured in hours, in what units is the standard error of estimate measured?

A) 0.49; it decreases; hours
B) 0.49; it decreases; hours squared
C) 0.49; it increases; hours
D) 0.8367; it decreases; hours
E) 0.8367; it increases; hours squared

Question 77

Which of the following statements regarding the coefficient of correlation is true?

A) It ranges from -1.0 to +1.0 inclusive
B) It measures the strength of the relationship between two variables
C) A value of 0.00 indicates two variables are not related
D) All of these statements are correct
E) None of these statements are correct

Question 78

If r = 0.65, what does the coefficient of determination equal?

A) 0.194
B) 0.423
C) 0.577
D) 0.806
E) None of these statements are correct

Question 79

If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?

A) Not related
B) Dependent on each other
C) Highly related
D) All of these statements are correct
E) None of these statements are correct

Question 80

What does a coefficient of correlation of 0.70 infer?

A) Almost no correlation because 0.70 is close to 1.0
B) 70% of the variation in one variable is explained by the other
C) Coefficient of determination is 0.49
D) Coefficient of nondetermination is 0.30
E) None of these statements are correct