Deck 13: Correlation and Linear Regression

Question 1

The values of a and b in the regression equation are called the regression coefficients.

Answer 1

True

Question 2

An economist is interested in predicting the unemployment rate based on gross domestic product. Because the economist is interested in predicting unemployment,the independent variable is gross domestic product.

Answer 2

True

Question 3

In regression analysis,error is defined as ( - Y).

Answer 3

False

Question 4

The coefficient of determination is the square root of the coefficient of correlation.

Question 5

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

A)A scatter diagram
B)A bar chart
C)A pie chart
D)A histogram

Question 6

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

Question 7

What does a coefficient of correlation of 0.70 infer?

A)There is almost no correlation because 0.70 is close to 1.0.
B)Seventy percent of the variation in one variable is explained by the other variable.
C)The coefficient of determination is 0.49.
D)The coefficient of nondetermination is 0.30.

Question 8

Because the coefficient of determination is expressed as a percent,its value is between 0% and 100%.

Question 9

The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.

Question 10

One assumption underlying linear regression is that the X values are normally distributed.

Question 11

The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

Question 12

The standard error of estimate measures the accuracy of a prediction.

Question 13

In regression analysis,what is the predictor variable called?

A)Independent variable
B)Dependent variable
C)Correlation variable
D)Variable of determination

Question 14

The hypothesis to test the slope of a regression equation is H₀: α = 0.

Question 15

The coefficient of determination is the proportion of total variation in Y that is explained by X.

Question 16

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.

Question 17

A scatter diagram is a graph that portrays the correlation between a dependent variable and an independent variable.

Question 18

Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables.

Question 19

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

A)It ranges from 0.0 to + 1.0 inclusive.
B)It describes the relationship between two variables.
C)A value of 0.00 indicates two variables are related.
D)It is calculated as the square of the slope.

Question 20

A confidence interval can be determined for the mean value of Y for a given value of X.

Question 21

If the coefficient of determination is 0.94,what can we say about the relationship between two variables?

A)The strength of the relationship is 0.94.
B)The direction of the relationship is positive.
C)Ninety-four percent of the total variation of the dependent variable is explained by the independent variable.
D)The direction of the relationship is negative.

Question 22

In the regression equation,what does the letter Y represent?

A)The Y-intercept
B)The slope of the line
C)The independent variable
D)The dependent variable

Question 23

What is the test statistic to test the significance of the slope in a regression equation?

A)z-statistic
B)F-statistic
C)t-statistic
D)π-statistic

Question 24

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

A)The variables are not related.
B)The variables are dependent on each other.
C)The variables are highly related.
D)X causes Y.

Question 25

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

A)0.9412
B)0.0121
C)0.7921
D)0.1100

Question 26

What is the null hypothesis to test the significance of the slope in a regression equation?

A)H₀: β = 0
B)H₀: β ≠ 0
C)H₀: β ≤ 0
D)H₀: β ≥ 0

Question 27

The regression equation is Ŷ = 29.29 − 0.96X,the sample size is 8,and the standard error of the slope is 0.22. What is the test statistic to test the significance of the slope?

A)z = −4.364
B)z = +4.364
C)t = −4.364
D)t = −0.960

Question 28

The regression equation is Ŷ = 29.29 − 0.96X,the sample size is 8,and the standard error of the slope is 0.22. What is the critical value to test the significance of the slope at the 0.01 significance level?

A)z = +2.576
B)z = +3.707
C)t = +3.355
D)t = ±3.707

Question 29

If we reject the null hypothesis,H₀: ρ = 0 ,what can we conclude about the population correlation coefficient?

A)It is zero.
B)It could be zero.
C)It is not zero.
D)It equals the computed sample correlation.

Question 30

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

A)strong
B)moderate
C)weak
D)zero

Question 31

What is the range of values for the coefficient of determination?

A)−1 to +1 inclusive
B)−100% to +100% inclusive
C)−100% to 0% inclusive
D)0% to 100% inclusive

Question 32

The Pearson product-moment correlation coefficient,r,requires that variables be measured with ________.

A)an interval or ratio scale
B)an ordinal or ratio scale
C)a nominal or ordinal scale
D)a nominal or ratio scale

Question 33

A hypothesis test is conducted at the 0.05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60,what is the computed value of the test statistic? Round to two decimal places.

A)1.96
B)2.07
C)2.94
D)3.60

Question 34

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

A)0.1945
B)0.4225
C)0.5778
D)0.8061

Question 35

What is the alternate hypothesis to test the significance of the slope in a regression equation?

A)H₁: β = 0
B)H₁: β ≠ 0
C)H₁: β ≤ 0
D)H₁: β ≥ 0

Question 36

In the regression equation,what does the letter b represent?

A)The Y-intercept
B)The slope of the line
C)Any value of the independent variable that is selected
D)The value of Y when X = 0

Question 37

Which value of r indicates a stronger correlation than 0.40?

A)−0.30
B)−0.80
C)+0.38
D)0

Question 38

In the regression equation,what does the letter a represent?

A)The Y-intercept
B)The slope of the line
C)Any value of the independent variable that is selected
D)An error

Question 39

What are the degrees of freedom used to test the significance of the slope in a simple linear regression equation?

A)n − 1
B)n − 2
C)n − 1,n − 2
D)(n − 1)(n − 2)

Question 40

In the regression equation,what does the letter X represent?

A)The Y-intercept
B)The slope of the line
C)The independent variable
D)The dependent variable

Question 41

Which of the following is the same between a confidence interval and a prediction interval?

A)The formulas are the same.
B)They both use the standard error of estimate.
C)They both provide a confidence interval for the mean.
D)A confidence interval and prediction interval are the same width.

Question 42

Which of the following is true about the standard error of estimate?

A)It is a measure of the accuracy of the prediction.
B)It is based on squared vertical deviations between Y and X.
C)It can be negative.
D)It is calculated using the regression mean square.

Question 43

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?

A)Salesperson
B)Number of contacts
C)Amount of sales
D)Sales manager

Question 44

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

A)When X = 0,Y = 10.
B)X increases by 10 for each unit increase in Y.
C)Y increases by 10 for each unit increase in X.
D)It is the error of estimation.

Question 45

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the slope of the linear equation?

A)−12.201
B)2.195
C)−1.860
D)12.505

Question 46

The regression equation is Ŷ = 30 + 2.56X,the sample size is 14,and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level?

A)z = ±1.96
B)t = ±2.179
C)t = ±2.145
D)t = +2.145

Question 47

Which of the following are true assumptions underlying linear regression? (1)For each value of X,there is a group of Y values that is normally distributed.
(2)The means of these normal distributions of Y values all lie on the regression line.
(3)The standard deviations of these normal distributions are equal.

A)Only (1)
B)Only (2)
C)Only (3)
D)All of them

Question 48

If all the plots on a scatter diagram lie on a straight line,what is the standard error of estimate?

A)−1
B)+1
C)0
D)Infinity

Question 49

What is the general form of the regression equation?

A) = ab
B) = a + (bX)
C) = (a + b)X
D) = abX

Question 50

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the Y-intercept of the linear equation?

A)−12.201
B)2.195
C)−1.860
D)12.505

Question 51

In the least squares equation, = 10 + 20X,the value of 20 indicates ________.

A)the Y-intercept increases by 20 units for each unit increase in X
B)that Y increases by 20 units for each unit increase in X
C)that X increases by 20 units for each unit increase in Y
D)the error in prediction

Question 52

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the dependent variable?

A)Salesperson
B)Number of contacts
C)Amount of sales dollars
D)Sales manager

Question 53

Based on the regression equation,we can ________.

A)predict the value of the dependent variable given a value of the independent variable
B)predict the value of the independent variable given a value of the dependent variable
C)measure the association between two variables
D)measure cause and effect

Question 54

When comparing the 95% confidence and prediction intervals for a given regression analysis ________.

A)the confidence interval is wider than a prediction interval
B)the confidence interval is narrower than a prediction interval
C)there is no difference between confidence and prediction intervals
D)the prediction interval has a higher level of confidence

Question 55

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

A)It is the slope of the line.
B)It is the Y-intercept.
C)It is the predicted value of Y,given a specific X value.
D)It is the value of Y when X = 0.

Question 56

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the standard error of the slope?

A)0.176
B)6.560
C)−12.201
D)12.505

Question 57

In regression,the difference between the confidence interval and prediction interval formulas is ________.

A)the prediction interval is the square root of the confidence interval
B)the addition of 1 to the quantity under the radical sign
C)the prediction interval uses r² and the confidence interval uses r
D)no difference

Question 58

The regression equation is Ŷ = 30 + 2.56X,the sample size is 14,and the standard error of the slope is 0.97. What is the test statistic to test the significance of the slope?

A)z = −2.560
B)z = +2.639
C)t = +2.560
D)t = +2.639

Question 59

What is the variable used to predict another variable called?

A)Independent variable
B)Dependent variable
C)Important variable
D)Causal variable

Question 60

Given the least squares regression equation, = 1,202 + 1,133X,when X = 3,what does equal?

A)5,734
B)8,000
C)4,601
D)4,050

Question 61

The value of the correlation coefficient (r)________.

A)can be equal to the value of the coefficient of determination (r²)
B)can never be equal to the value of the coefficient of determination (r²)
C)can range from −2.0 to +2.0
D)is generally larger than the value of the coefficient of determination

Question 62

Using the following information: What is the standard error of the estimate?

A)136.8552
B)1094.842
C)11.6985
D)13418.4

Question 63

Using the following information: The regression analysis can be summarized as follows:

A)No significant relationship exists between the variables.
B)A significant negative relationship exists between the variables.
C)A significant positive relationship exists between the variables.
D)For every unit increase in X,Y decreases by 12.8094.

Question 64

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: = 33.4. = 2,814.4. The 95% prediction interval for a particular person making 30 calls is ________.

A)55.8,51.5
B)51.4,55.9
C)46.7,60.6
D)31.1,76.2

Question 65

Using the following information: If testing the hypothesis H₀: ρ = 0,the computed t-statistic is ________.

A)9.49
B)8.84
C)8.18
D)Cannot be computed

Question 66

Using the following information: What is the coefficient of determination? Round the percentage to one decimal point.

A)91.8%
B)8.2%
C)90.0%
D)136.9%

Question 67

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: What is the value of the coefficient of correlation?

A)+0.6317
B)+0.9754
C)−0.9754
D)+0.9513

Question 68

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the regression equation?

A) = 2.195 − 12.201X
B) = −12.201 + 2.195X
C) = 12.201 + 2.195X
D) = 2.195 + 12.201X

Question 69

Consider a regression analysis,where the correlation coefficient is 0.18. Then,the coefficient of determination is ________.

A)0.36
B)0.0324
C)0.424
D)1.16

Question 70

Using the following information: Estimate the value of when X = 4.

A)10.45
B)3.73
C)8.718
D)−4.092

Question 71

Consider the following regression analysis between sales (Y in $1,000)and social media advertising (X in dollars). = 55,000 + 7X The regression equation implies that an ________.

A)increase of $7 in advertising is associated with an increase of $7,000 in sales
B)increase of $1 in advertising is associated with an increase of $7 in sales
C)increase of $1 in advertising is associated with an increase of $62,000 in sales
D)increase of $1 in advertising is associated with an increase of $7,000 in sales

Question 72

A regression analysis yields the following information: = 2.21 + 1.49X; n = 10; = 166; = 32; = 134; = 31.6. Compute the 95% confidence interval when X = 4.

A)0.0,4.05
B)4.15,12.25
C)2.67,5.33
D)6.842,9.497

Question 73

Using the following information: The regression equation is ________.

A) = 2.1794 − 12.8094X
B) = −12.8094 + 2.1794X
C)12.8094X = 2.1794
D)X = −12.8094 + 2.1794

Question 74

A regression analysis yields the following information: = 2.21 + 1.49X; n = 10; = 166; = 32; = 134; = 31.6. Compute the 95% prediction interval when X = 4.

A)0.0,4.05
B)2.67,5.33
C)4.118,12.226
D)6.873,9.527

Question 75

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: = 33.4. = 2814.4. Rounding to one decimal place,the 95% confidence interval for 30 calls is ________.

A)55.8,51.5
B)51.4,55.9
C)46.7,60.6
D)31.1,76.2

Question 76

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: What is the value of the coefficient of determination?

A)−0.9513
B)0.9754
C)0.6319
D)0.9513

Question 77

Using the following information: What is the correlation coefficient?

A)0.9184
B)0.9583
C)−0.9583
D)0.9004

Question 78

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: What is the value of the standard error of estimate?

A)9.310
B)8.778
C)8.328
D)86.68

Question 79

Consider a regression and correlation analysis where r² = 1. We know that ________.

A)SSE must be greater than one
B)SSE must be greater than SS Total
C)SSE can take on any negative or positive value
D)SSE must equal to zero

Question 80

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the decision regarding the hypothesis if the p-value for the slope equals zero?

A)Fail to reject the null hypothesis.
B)Fail to reject the alternative hypothesis.
C)Reject the null hypothesis.
D)Reject the alternative hypothesis.