Deck 18: Correlation and Regression

Question 1

The first step involved in conducting bivariate analysis is the development of a scatter diagram.

Answer 1

True

Question 2

The correlation coefficient between two variables will be the same regardless of their underlying units of measurement.

Answer 2

True

Question 3

A procedure for deriving a mathematical relationship, in the form of an equation, between a single metric dependent variable and a single metric independent variable is called univariate regression.

Answer 3

False

Question 4

According to the text, a scatter diagram is also known as a scattergram.

Question 5

The final step involved in conducting bivariate analysis is significance testing.

Question 6

The product moment correlation is also referred to as regression correlation.

Question 7

Regression analysis is a statistical procedure for analyzing associative relationships between a metric dependent variable and one or more independent variables.

Question 8

Regression analysis is concerned with the nature and degree of association between variables and does not imply or assume any causality.

Question 9

Questionnaire development is a step involved in conducting bivariate regression analysis.

Question 10

The covariance correlation is the most widely used statistic that summarizes the strength and direction of association between two metric variables.

Question 11

A systematic relationship between two variables in which a change in one implies a corresponding change in the other is called covariance.

Question 12

The correlation coefficient between two variables varies depending on their underlying units of measurement.

Question 13

The r² statistic measures the proportion of variation in one variable that is explained by the other.

Question 14

The covariance may be either positive or negative.

Question 15

The test statistic for evaluating the null hypothesis associated with the product moment correlation is the F-test.

Question 16

Both r and r² are symmetric measures of association. In other words, the correlation of X and Y is the same as the correlation of Y and X.

Question 17

A scatter diagram is a plot of the values of two variables for all the cases or observations.

Question 18

A statistic summarizing the strength of association between two metric variables is called the product moment correlation.

Question 19

When r = 0, this means that X and Y are unrelated.

Question 20

When determining the correlation coefficient, r, it does matter which variable is considered to be the dependent variable and which the independent.

Question 21

To estimate the accuracy of predicted values, it is useful to calculate the standard error of estimate.

Question 22

A technique for fitting a straight line to a scattergram by minimizing the vertical distances of all the points from the line is called the most-squares procedure.

Question 23

When data are standardized, the intercept assumes a value of one.

Question 24

The distances for all the points from the regression line are squared and added together to arrive at the sum of the squared errors, which is a measure of total error.

Question 25

In multiple regression, if the overall null hypothesis is rejected, we know which specific coefficients
(βᵢs) are nonzero.

Question 26

Standardization may be desirable because it is easier to compare the beta coefficients than it is to compare the raw coefficients.

Question 27

The standardized regression coefficient is the slope obtained by the regression of y on x when the data are standardized.

Question 28

The strength of association is measured by the coefficient of determination.

Question 29

The process by which the raw data are transformed into new variables that have a mean of 0 and a variance of 1 is called standardization.

Question 30

Multiple regression is a statistical technique that simultaneously develops a mathematical relationship between two or more independent variables and an interval-scaled dependent variable.

Question 31

To standardize a variable, simply subtract the mean and divide the difference by the standard deviation.

Question 32

An equation used to explain the results of multiple regression analysis is called the multiple regression model.

Question 33

The vertical distance from a point to the regression line is the squared error, eⱼ².

Question 34

According to the text, the beta coefficient is also called the beta weight.

Question 35

The difference between the observed value of Y and the value predicted by the regression equation is called the standard error.

Question 36

The term used to denote the standardized regression coefficient is called the alpha coefficient.

Question 37

The most commonly used technique for fitting a straight line to a scattergram is the least-squares procedure.

Question 38

The best fitting line on a scattergram is called the covariance.

Question 39

The non-standardized regression coefficient indicates the expected change in Y when X is changed by one unit.

Question 40

In bivariate regression, the null hypothesis is that no linear relationship exists between X and Y, or H₀: β₁ = 0.

Question 41

R² cannot decrease as more independent variables are added to the regression equation.

Question 42

The multiple correlation coefficient, R, can also be viewed as the simple correlation coefficient, r, between Y and Ŷ.

Question 43

Which of the following is NOT a step involved in conducting bivariate regression analysis?

A) estimation of parameters
B) questionnaire development
C) significance testing
D) prediction accuracy
E) examination of residuals

Question 44

All of the following are terms used in regression analysis that arise from the mathematical relationship between the variables EXCEPT:

A) dependent variables.
B) criterion variable.
C) predictor variables.
D) standard variables.
E) independent variables.

Question 45

The product moment correlation is also referred to as all of the following EXCEPT:

A) simple correlation.
B) bivariate correlation.
C) correlation coefficient.
D) Pearson correlation.
E) F-statistic.

Question 46

All of the following are true EXCEPT:

A) The product moment correlation is denoted by ρ.
B) The coefficient r is an estimator of ρ.
C) The calculation of r assumes X and Y are metric.
D) Data that use rating scales with a small number of categories will tend to under estimate ρ.
E) Data that use rating scales with a small number of categories will tend to over estimate ρ.

Question 47

________ is concerned with the nature and degree of association between variables and does not imply or assume any causality.

A) Regression analysis
B) Analysis of variance
C) Deviation analysis
D) F-test
E) Functional linear analysis

Question 48

A procedure for deriving a mathematical relationship, in the form of an equation, between a single metric dependent variable and a single metric independent variable is called ________.

A) univariate regression
B) bivariate regression
C) multivariate regression
D) parallel regression
E) pairwise regression

Question 49

It is not possible to conduct correlation and regression analysis if the data collected in social media are qualitative in nature.

Question 50

Which of the following is (are) true?

A) r² = explained variation / total variation
B) r² = SSx / SSy
C) r² = (total variation - error variation) / total variation
D) r² = (SSy - SSerror) / SSy
E) All of the above are true.

Question 51

A statistic summarizing the strength of association between two metric variables is called the ________.

A) product moment correlation
B) covariance correlation
C) inverse correlation
D) bivariate correlation
E) F-statistic

Question 52

Which of the following statistics indicates the degree to which the variation in one variable, X, is related to the variation in another variable, Y?

A) covariance correlation
B) inverse correlation
C) product moment correlation
D) bivariate correlation
E) F-statistic

Question 53

A(n) ________ is a plot of the values of two variables for all the cases or observations.

A) scatter diagram
B) regression line
C) covariance chart
D) distribution curve
E) observational plot

Question 54

According to the text, a scatter diagram is also known as a ________.

A) histogram
B) pictogram
C) scattergram
D) pie chart
E) box and whiskers diagram

Question 55

In multiple regression, the strength of association is measured by the square of the multiple correlation coefficient, which is called the coefficient of multiple determination.

Question 56

________ is a statistical procedure for analyzing associative relationships between a metric dependent variable and one or more independent variables.

A) Regression analysis
B) Covariance analysis
C) Deviation analysis
D) Correlation analysis
E) Functional linear analysis

Question 57

Significance testing involves testing the significance of the overall regression equation as well as specific partial regression coefficients.

Question 58

Regression analysis of an independent and dependent variable can be used in all of the following ways EXCEPT:

A) determining whether a relationship exists.
B) assessing the strength of relationship.
C) determining the structure or form of the relationship.
D) predicting values of the dependent variable.
E) determining causality.

Question 59

A systematic relationship between two variables in which a change in one implies a corresponding change in the other is called ________.

A) causation
B) analysis of variance
C) covariance
D) deviation
E) standard deviation

Question 60

The ________ is the most widely used statistic that summarizes the strength and direction of association between two metric variables.

A) covariance correlation
B) product moment correlation
C) inverse correlation
D) bivariate correlation
E) F-statistic

Question 61

To standardize a variable, simply subtract the mean and divide the difference by the ________.

A) variance
B) correlation coefficient
C) residual
D) standard deviation
E) mean

Question 62

The difference between the observed value of Y and the value predicted by the regression equation is called the ________.

A) correlation coefficient
B) residual
C) standard error
D) random error
E) total error

Question 63

According to the text, the beta coefficient is also called the ________.

A) beta factor
B) beta variable
C) beta element
D) beta weight
E) beta carotene

Question 64

The distances for all the points on the regression line are squared and added together to compute the ________, which is a measure of total error.

A) correlation errors
B) standard error of the mean
C) sum of the squared errors
D) random distribution error
E) distance log

Question 65

When data are standardized, the intercept assumes a value of ________.

A) one
B) negative one
C) infinity
D) zero
E) positive one

Question 66

In multiple regression, the strength of association is measured by the square of the multiple correlation coefficient, which is called the ________.

A) coefficient of multiple determination
B) variance
C) standard error of the mean
D) standard deviation
E) squared deviation

Question 67

________ is a statistical technique that simultaneously develops a mathematical relationship between two or more independent variables and an interval-scaled dependent variable.

A) Product moment correlation
B) Standard regression
C) Factor analysis
D) Multiple regression
E) Canonical correlation

Question 68

To estimate the accuracy of predicted values, it is useful to calculate the ________.

A) analysis of variance
B) correlation coefficient
C) standard error of estimate
D) residual
E) precision coefficient

Question 69

The best fitting line on a scattergram is called the ________.

A) regression line
B) correlation coefficient
C) covariance
D) standard error
E) plumb line

Question 70

The most commonly used technique for fitting a straight line to a scattergram is the ________.

A) most-squares procedure
B) analysis of variance
C) least-squares procedure
D) correlation equation
E) sum of squared errors

Question 71

The strength of association is measured by the ________.

A) coefficient of determination
B) regression equation
C) correlation coefficient
D) F factor
E) F-statistic

Question 72

________ may be desirable because it is easier to compare the beta coefficients than it is to compare the raw coefficients.

A) Covariance
B) Standardization
C) Correlation
D) Regression
E) Analysis of variance

Question 73

The null hypothesis in bivariate regression is ________.

A) Bᵧₓ = Bₓᵧ = rₓᵧ
B) B = Covₓᵧ / sₓ²
C) sₓ = xmₑₐn
D) a = xy
E) B₁ = 0

Question 74

The final step involved in conducting bivariate analysis is ________.

A) estimation of parameters
B) significance testing
C) examination of residuals
D) prediction accuracy
E) standard regression coefficient

Question 75

A technique for fitting a straight line to a scattergram by minimizing the sum of the squares of the vertical distances of all the points from the line is called the ________.

A) most-squares procedure
B) analysis of variance
C) least-squares procedure
D) correlation equation
E) vertical minimization algorithm

Question 76

The ________ coefficient is the slope obtained by the regression of y on x when the data are standardized.

A) random regression
B) standardized regression
C) bipolar regression
D) alternate regression
E) alpha

Question 77

The term used to denote the standardized regression coefficient is called the ________.

A) alpha coefficient
B) beta coefficient
C) gamma coefficient
D) theta coefficient
E) pi coefficient

Question 78

The process by which the raw data are transformed into new variables that have a mean of 0 and a variance of 1 is called ________.

A) standardization
B) covariance
C) correlation
D) regression
E) analysis of variance

Question 79

The first step involved in conducting bivariate analysis is the development of a ________.

A) regression line
B) covariance chart
C) scatter diagram
D) distribution curve
E) contingency table

Question 80

An equation used to explain the results of multiple regression analysis is called the ________.

A) product moment correlation model
B) multiple regression model
C) standard regression model
D) covariance model
E) unitary model