# Quiz 13: Correlation and Linear Regression

Statistics

Q 1Q 1

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

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True False

True

Q 2Q 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.

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True False

True

Q 3Q 3

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

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True False

True

Q 4Q 4

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

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True False

Q 5Q 5

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

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True False

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True False

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True False

Q 8Q 8

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

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True False

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True False

Q 10Q 10

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.

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True False

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True False

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True False

Q 13Q 13

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

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True False

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True False

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True False

Q 16Q 16

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

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Multiple Choice

Q 17Q 17

In regression analysis,what is the predictor variable called?
A)Independent variable
B)Dependent variable
C)Correlation variable
D)Variable of determination

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Multiple Choice

Q 18Q 18

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.

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Multiple Choice

Q 19Q 19

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.

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Multiple Choice

Q 20Q 20

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

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Multiple Choice

Q 21Q 21

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

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Multiple Choice

Q 22Q 22

If the correlation between two variables is close to one,the association between the variables is ________.
A)strong
B)moderate
C)weak
D)zero

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Multiple Choice

Q 23Q 23

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.

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Multiple Choice

Q 24Q 24

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.

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Multiple Choice

Q 25Q 25

If r = 0.65,what does the coefficient of determination equal?
A)0.1945
B)0.4225
C)0.5778
D)0.8061

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Multiple Choice

Q 26Q 26

What does the coefficient of determination equal if r = 0.89?
A)0.9412
B)0.0121
C)0.7921
D)0.1100

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Multiple Choice

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Multiple Choice

Q 28Q 28

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

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Multiple Choice

Q 29Q 29

If we reject the null hypothesis,H

_{0}: 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.Free

Multiple Choice

Q 30Q 30

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

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Multiple Choice

Q 31Q 31

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

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Multiple Choice

Q 32Q 32

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

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Multiple Choice

Q 33Q 33

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

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Multiple Choice

Q 34Q 34

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

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Multiple Choice

Q 35Q 35

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

_{0}: β = 0 B)H_{0}: β ≠ 0 C)H_{0}: β ≤ 0 D)H_{0}: β ≥ 0Free

Multiple Choice

Q 36Q 36

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

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Multiple Choice

Q 37Q 37

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)

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Multiple Choice

Q 38Q 38

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

_{1}: β = 0 B)H_{1}: β ≠ 0 C)H_{1}: β ≤ 0 D)H_{1}: β ≥ 0Free

Multiple Choice

Q 39Q 39

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

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Multiple Choice

Q 40Q 40

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

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Multiple Choice

Q 41Q 41

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

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Multiple Choice

Q 42Q 42

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

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Multiple Choice

Q 43Q 43

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

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Multiple Choice

Q 44Q 44

What is the general form of the regression equation?
A) = ab
B) = a + (bX)
C) = (a + b)X
D) = abX

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Multiple Choice

Q 45Q 45

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

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Multiple Choice

Q 46Q 46

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

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Multiple Choice

Q 47Q 47

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.

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Multiple Choice

Q 48Q 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

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Multiple Choice

Q 49Q 49

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

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Multiple Choice

Q 50Q 50

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.

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Multiple Choice

Q 51Q 51

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.

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Multiple Choice

Q 52Q 52

What is the variable used to predict another variable called?
A)Independent variable
B)Dependent variable
C)Important variable
D)Causal variable

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Multiple Choice

Q 53Q 53

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 r

^{2}and the confidence interval uses r D)no differenceFree

Multiple Choice

Q 54Q 54

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.

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Multiple Choice

Q 55Q 55

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

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Multiple Choice

Q 56Q 56

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

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Multiple Choice

Q 57Q 57

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

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Multiple Choice

Q 58Q 58

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

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Multiple Choice

Q 59Q 59

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

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Multiple Choice

Q 60Q 60

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

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Multiple Choice

Q 61Q 61

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.

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Multiple Choice

Q 62Q 62

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

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Multiple Choice

Q 63Q 63

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

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Multiple Choice

Q 64Q 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 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

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Multiple Choice

Q 65Q 65

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

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Multiple Choice

Q 66Q 66

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

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Multiple Choice

Q 67Q 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 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

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Multiple Choice

Q 68Q 68

Using the following information: What is the standard error of the estimate?
A)136.8552
B)1094.842
C)11.6985
D)13418.4

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Multiple Choice

Q 69Q 69

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%

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Multiple Choice

Q 70Q 70

Using the following information: What is the correlation coefficient?
A)0.9184
B)0.9583
C)−0.9583
D)0.9004

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Multiple Choice

Q 71Q 71

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

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Multiple Choice

Q 72Q 72

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.

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Multiple Choice

Q 73Q 73

Using the following information: If testing the hypothesis H

_{0}: ρ = 0,the computed t-statistic is ________. A)9.49 B)8.84 C)8.18 D)Cannot be computedFree

Multiple Choice

Q 74Q 74

Using the following information: Estimate the value of when X = 4.
A)10.45
B)3.73
C)8.718
D)−4.092

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Multiple Choice

Q 75Q 75

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

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Multiple Choice

Q 76Q 76

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

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Multiple Choice

Q 77Q 77

The value of the correlation coefficient (r)________.
A)can be equal to the value of the coefficient of determination (r

^{2}) B)can never be equal to the value of the coefficient of determination (r^{2}) C)can range from −2.0 to +2.0 D)is generally larger than the value of the coefficient of determinationFree

Multiple Choice

Q 78Q 78

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

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Multiple Choice

Q 79Q 79

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

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Multiple Choice

Q 80Q 80

Consider a regression and correlation analysis where r

^{2}= 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 zeroFree

Multiple Choice

Q 81Q 81

Consider the following regression equation: Y = 30 + 8X. If SSE = 720 and SS Total = 1,200,then the correlation coefficient is ________.
A)−0.632
B)0.70
C)0.632
D)−0.70

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Multiple Choice

Q 82Q 82

If the correlation coefficient has a negative value,then the coefficient of determination ________.
A)can take on either a negative or positive value
B)must be positive
C)will also have a negative value
D)will equal zero

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Multiple Choice

Q 83Q 83

In regression,if the relationship between the dependent and independent variables is nonlinear,a linear relationship between the variables can be achieved by ________.
A)including an interaction term
B)multiplying by 100
C)rescaling the variables
D)adding another independent variable

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Multiple Choice

Q 84Q 84

An example of a way to rescale a variable to create a linear relationship is ________.
A)dividing all the values of the dependent variable by 5
B)computing the log of all values of the dependent and independent variables
C)adding 50 to all of the values of the dependent and independent variables
D)adding the values of the dependent and independent variables to create a new dependent variable

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Multiple Choice