Deck 23: Bivariate Statistical Analysis: Measures of Association

Question 1

The least-squares regression line minimizes the sum of the squared deviations of the actual values from the predicted values in the regression line.

Answer 1

True

Question 2

Covariance is the extent to which one variable causes a change in another variable.

Answer 2

False

Question 3

In regression analysis, the equation of a straight line is Y = a + b X.

Answer 3

True

Question 4

In regression, the standardized Y-intercept term is always 0.

Question 5

In a correlation matrix, the main diagonal contains correlations of 1.00 because it represents a variable's correlation with itself.

Question 6

In a regression equation, the slope of the line, b, is the change in X that is due to a corresponding change of one unit of Y.

Question 7

Measure of association is a general term that refers to causality.

Question 8

A Spearman correlation is more appropriate for interval and ratio data than is the Pearson product-moment correlation.

Question 9

If r = -0.88, this indicates a weak relationship between the two variables under study.

Question 10

In simple regression, standardized parameter estimates reflect the measurement scale range.

Question 11

The correlation coefficient, r, indicates the magnitude of the linear relationships but not the direction of that relationship.

Question 12

In most business research, the estimate of b in a regression equation is most important.

Question 13

If the purpose of the regression analysis is forecasting, then standardized regression estimates must be used.

Question 14

One way to determine the relationship between X and Y is to simply visually draw the best-fit straight line through the points in the figure.

Question 15

A correlation coefficient is a measure of the covariance, or association, between two at-least interval variables.

Question 16

The ordinary least-squares method of regression analysis is based on the logic of how much better a regression line can predict values of Y compared to simply using the standard deviation as a prediction.

Question 17

The square of the correlation coefficient indicates the part of the total variance of dependent variable that can be accounted for by the independent variable.

Question 18

The statistical significance of a correlation can be tested using the t-test.

Question 19

A correlation matrix is the standard form for reporting observed correlations between two variables.

Question 20

The symbol for the Pearson product-moment correlation coefficient is b.

Question 21

A rule of thumb for R² is that it must be greater than 0.80 for a regression model to be significant.

Question 22

Which of the following represents the proportion of the total variance of a variable accounted for by another value of another variable?

A) product-moment correlation
B) correlation coefficient
C) F-test
D) coefficient of determination

Question 23

If the regression weight is in the hypothesized direction, the hypothesis is supported.

Question 24

A(n) _____ is a statistical measure of the covariation, or association, between two at-least interval variables.

A) alpha coefficient
B) beta coefficient
C) correlation coefficient
D) c²

Question 25

A bivariate statistical technique that is used to measure the strength of the relationship between two variables is called a _____.

A) one-group t-test
B) two-group t-test
C) measure of association
D) correlation matrix

Question 26

When the on-time performance of airlines is used to predict the number of customer complaints in a regression equation, on-time performance is the ______ variable and the number of customer complaints is the ______ variable.

A) independent; dependent
B) dependent; dependent
C) dependent; independent
D) independent; predictor

Question 27

The coefficient of determination reflects the proportion of variance that can be explained by the regression line.

Question 28

Which of the following is the standard form for reporting observed correlations among multiple variables?

A) correlation matrix
B) contingency table
C) Pearson grid
D) inverse table

Question 29

If the correlation coefficient is - 0.62, the coefficient of determination is approximately:

A) + 0.38
B) + 0.62
C) - 0.38
D) - 0.23

Question 30

If the correlation between X and Y is -0.72, approximately what percentage of the variance in Y can be explained by X?

A) 52 percent
B) 72 percent
C) 85 percent
D) 28 percent

Question 31

The first step in interpreting simple regression output is to interpret the individual parameter coefficient.

Question 32

When the correlation between two variables is +0.92, this means that as one variable ______ , the other variable ______.

A) decreases; increases
B) increases; stays the same
C) increases; increases
D) decreases; stays the same

Question 33

In a correlation matrix, the correlations in the main diagonal are all equal to _____.

A) -1.00
B) 0
C) +0.50
D) +1.00

Question 34

The Pearson product-moment correlation requires what type of scale for the data?

A) nominal
B) interval
C) ordinal
D) all of these choices

Question 35

If there is no relationship between two variables, the correlation coefficient between them would be _____.

A) +1.0
B) -1.0
C) +0.50
D) 0

Question 36

The statistical significance of a regression model is determined by a F-test.

Question 37

The _____ is a measure obtained by squaring the correlation coefficient.

A) t-statistic
B) coefficient of determination (R²)
C) F-ratio
D) Pearson coefficient

Question 38

If the correlation between two variables is - 0.85, this means that ____.

A) there is a weak positive relationship between the variables
B) there is a strong inverse relationship between the variables
C) there is a weak negative relationship between the variables
D) there is a strong positive relationship between the variables

Question 39

The extent to which a change in one variable corresponds systematically to a change in another is called _____.

A) spurious association
B) significance
C) covariance
D) standardized coefficient

Question 40

The Pearson product-moment correlation coefficient ranges between _____.

A) zero and +1.0
B) -1.0 and zero
C) -1.0 and +1.0
D) -2.0 and +2.0

Question 41

In the regression equation, Y = a + b X, a is the symbol for the _____.

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

Question 42

In the regression equation, Y = a + b X, Y is the _____.

A) dependent variable
B) slope
C) independent variable
D) Y-intercept

Question 43

The statistical measure of the association between two variables is known as the ______ coefficient.

Question 44

The Pearson product-moment correlation requires at least ______ data.

Question 45

What is the first step in interpreting a simple regression output?

A) interpret the individual parameter estimates
B) determine the degrees of freedom
C) look at the c² to see if it is significant
D) interpret the overall significance of the model

Question 46

If the regression equation is: Y = -4.2 + 3.6 X , then the expected score for Y when X is 4 would be _____.

A) -18.6
B) 10.2
C) 18.6
D) 4

Question 47

If the number of coupons given out at shopping malls is used to predict the number of tickets that will be sold to a country and western band's performance at a local club, the number of coupons is the ______ variable.

Question 48

Which regression estimation technique is based on the logic of how much better a regression line can predict values of Y compared to simply using the mean as a prediction for all observations no matter what the value of X may be?

A) visual estimation
B) maximum likelihood
C) coefficient of determination
D) ordinary least squares (OLS)

Question 49

Which of the following is most appropriate if the purpose of the regression analysis is forecasting?

A) standardized regression coefficient (b)
B) Y-intercept a
C) coefficient of determination (R²)
D) raw parameter estimates

Question 50

In the regression equation, Y = a + b X , b is the _____.

A) y-intercept
B) independent variable
C) slope of the regression line
D) dependent variable

Question 51

If the regression equation is: Y = 24.35 - 14.2 X , then 24.35 is the ______ , while -14.2 is the ______.

A) slope; y-intercept
B) independent variable; slope
C) dependent variable; y-intercept
D) Y-intercept; slope

Question 52

In regression analysis, the symbol X is commonly used for the ______ variable, and the symbol Y is commonly used for the ______ variable.

A) dependent; moderating
B) independent; dependent
C) dependent; independent
D) independent; moderating

Question 53

In regression analysis, the dependent variable is also called the _____ variable.

A) predictor
B) exogenous
C) criterion
D) internal

Question 54

All of the following are simple regression estimation techniques EXCEPT _____.

A) chi-square estimation
B) maximum likelihood
C) visual estimation
D) ordinary least squares (OLS)

Question 55

Regression is a(n) _____ technique whereas correlation is a(n) _____ technique.

A) dependence; interdependence
B) interdependence; dependence
C) primary; secondary
D) univariate; bivariate

Question 56

If the t-test is used to test the significance of a correlation coefficient, it is hypothesized that _____.

A) r = +1.00
B) r = 0
C) r = -1.00
D) r = 100

Question 57

The extent to which a change in one variable corresponds systematically to a change in another is referred to as _____.

Question 58

The statistical significance of a regression model is determined using which test?

A) t-test
B) c²
C) F-test
D) Z-test

Question 59

Which of the following provides a common metric allowing regression results to be compared to one another no matter what the original scale range may have been?

A) standardized regression coefficient (b)
B) c²
C) coefficient of determination (R²)
D) raw parameter estimates

Question 60

Lance is studying the relationship between sales training of the sales force and customer satisfaction and loyalty. When researchers like Lance are focused on explanation rather than prediction, then which of the following is most appropriate when using simple regression?

A) standardized regression coefficient (b)
B) Y-intercept a
C) c²
D) raw parameter estimates

Question 61

The square of the correlation coefficient is called the _____.

Question 62

Covariation in which the association between variables is in the opposite direction indicates a(n) _____ relationship.

Question 63

In a correlation matrix, the values in the main diagonal equal ______.

Question 64

In a regression equation, the slope of the regression line is denoted by the symbol ______.

Question 65

The standard format for reporting the correlations between several variables is called the ______.

Question 66

The symbol for the coefficient of determination is _____.

Question 67

Explain how regression differs from correlation.

Question 68

A correlation coefficient indicates both the ______ of the relationship between two variables and the ______ of this relationship.

Question 69

Compare and contrast correlation, covariance, and causation.

Question 70

The technique use in regression analysis that guarantees that the resulting straight line will produce the least possible total error in using X to predict Y is called the _____ method.

Question 71

_____ regression estimates should be used when the researcher is testing explanatory hypotheses.

Question 72

Explain the ordinary least-squares (OLS) method of regression analysis and the logic behind it.

Question 73

Discuss the pros and cons of raw regression estimates and standardized regression estimates and discuss when each is appropriate.

Question 74

The Pearson product-moment correlation coefficient ranges between ______ and ______.

Question 75

The regression parameter that represents the height of the regression line relative to horizontal is _____.

Question 76

The first step in interpreting a simple regression output is to interpret the significance of the _____.

Question 77

Discuss the common procedures for testing association for data that are nominal, ordinal, and interval/ratio.

Question 78

If the correlation between two variables is -.55, the coefficient of determination is approximately ______.

Question 79

If the purpose of the regression analysis is forecasting, then _____ parameter estimates must be used.

Question 80

In testing for the significance of a correlation, it is hypothesized that the correlation is equal to ______.