Question 1

What is the relationship between a first-order and a zero-order correlation?

Accepted Answer

A)  The first-order correlation is based on the zero-order correlation but modifies the original bivariate association to account for a third variable. 
B)  The first-order correlation is the bivariate correlation between X1 and Y, and the zero-order correlation is the bivariate correlation between X1 and X2. 
C)  The first-order correlation is the bivariate correlation between X1 and X2, and the zero-order correlation is the bivariate correlation between X2 and Y. 
D)  Both are synonyms for the same thing. 
A)  The first-order correlation is based on the zero-order correlation but modifies the original bivariate association to account for a third variable. 
B)  The first-order correlation is the bivariate correlation between X1 and Y, and the zero-order correlation is the bivariate correlation between X1 and X2. 
C)  The first-order correlation is the bivariate correlation between X1 and X2, and the zero-order correlation is the bivariate correlation between X2 and Y. 
D)  Both are synonyms for the same thing. A

Question 2

Which of the following is the value of a (the Y intercept) after scores have been standardized?

Accepted Answer

A)  always 1 
B)  always R2 
C)  always b1 - b2 
D)  always 0 
A)  always 1 
B)  always R2 
C)  always b1 - b2 
D)  always 0 D

Question 3

Why is comparison of the separate effects of multiple independent variables often a challenge in multiple regression?

Accepted Answer

A)  Partial slopes fail to control for the effects of other X variables. 
B)  Multiple regression can handle only two X variables per equation. 
C)  Different independent variables usually have different units of measurement. 
D)  Linear associations may be positive or negative. 
A)  Partial slopes fail to control for the effects of other X variables. 
B)  Multiple regression can handle only two X variables per equation. 
C)  Different independent variables usually have different units of measurement. 
D)  Linear associations may be positive or negative. C

Question 4

In which of these scenarios would a standardized multiple regression equation be least useful?

Accepted Answer

A)  Y is happiness, ranging from 1 to 100; X1 is age, ranging from 18 to 85; X2 is household income, ranging from 0 to $450,000. 
B)  Y is personal income, ranging from $11,000 to $198,000; X1 is university science grade point average, ranging from 1 to 4; X2 is university non-science grade point average, ranging from 1 to 4. 
C)  Y is personal income, ranging from 0 to $275,000; X1 is height in cm, ranging from 149 to 210; X2 is body mass index, ranging from 16 to 45. 
D)  Y is number of children in household, ranging from 0 to 8; X1 is age, ranging from 18 to 85, X2 is number of cars owned by household, ranging from 0 to 8. 
A)  Y is happiness, ranging from 1 to 100; X1 is age, ranging from 18 to 85; X2 is household income, ranging from 0 to $450,000. 
B)  Y is personal income, ranging from $11,000 to $198,000; X1 is university science grade point average, ranging from 1 to 4; X2 is university non-science grade point average, ranging from 1 to 4. 
C)  Y is personal income, ranging from 0 to $275,000; X1 is height in cm, ranging from 149 to 210; X2 is body mass index, ranging from 16 to 45. 
D)  Y is number of children in household, ranging from 0 to 8; X1 is age, ranging from 18 to 85, X2 is number of cars owned by household, ranging from 0 to 8.

Question 5

X has a causal influence on Y, even after Z is controlled. What is the term for this relationship between X and Y?

Accepted Answer

A)  partial correlation relationship 
B)  direct relationship 
C)  spurious relationship 
D)  intervening relationship 
A)  partial correlation relationship 
B)  direct relationship 
C)  spurious relationship 
D)  intervening relationship

Question 6

Consider a multiple regression equation predicting life expectancy in a random sample of 35 countries. X1 is per capita GDP and X2 is the country's homicide rate (per 100,000). Suppose the regression equation is Y = a + 0.5(X1) - 0.08(X2). How should we interpret a?

Accepted Answer

A)  It is the predicted life expectancy value when a country has a GDP of 0 and a homicide rate of 0. 
B)  It is the predicted life expectancy value for a country with an average-level GDP and an average homicide rate. 
C)  It is the partial correlation between GDP and homicide rate. 
D)  It is the proportion of the variance in life expectancy explained by GDP and homicide rate. 
A)  It is the predicted life expectancy value when a country has a GDP of 0 and a homicide rate of 0. 
B)  It is the predicted life expectancy value for a country with an average-level GDP and an average homicide rate. 
C)  It is the partial correlation between GDP and homicide rate. 
D)  It is the proportion of the variance in life expectancy explained by GDP and homicide rate.

Question 7

How many variables can be used in a multiple regression equation?

Accepted Answer

A)  At least one intercept and at least one independent variable can be used. 
B)  No more than two independent variables can be used. 
C)  It depends on whether the dependent variable is interval-ratio or a nominal level of measurement. 
D)  Any number of independent variables can be used. 
A)  At least one intercept and at least one independent variable can be used. 
B)  No more than two independent variables can be used. 
C)  It depends on whether the dependent variable is interval-ratio or a nominal level of measurement. 
D)  Any number of independent variables can be used.

Question 8

In this least-squares regression equation, Y = a + b1X1 + b2X2, what represents the partial slopes?

Accepted Answer

A)  y and a 
B)  the sum of b1X1 and b2X2 
C)  the xs 
D)  the bs 
A)  y and a 
B)  the sum of b1X1 and b2X2 
C)  the xs 
D)  the bs

Question 9

A standardized multiple regression equation yields a beta weight of 0.65 for X1 and -0.50 for X2. Which of the following is an interpretation of X1's beta weight?

Accepted Answer

A)  A one standard deviation change in X1 is associated with a 0.65 standard deviation in Y, controlling for the effect of X2. 
B)  A one unit change in X1 is associated with a 0.65 standard deviation in X2, controlling for the effect of Y. 
C)  A one standard deviation change in X2 is associated with a 0.65 standard deviation change in Y, controlling for the effect of X1. 
D)  There is an error in this equation: beta-weights for X1 and X2 cannot have opposite signs. 
A)  A one standard deviation change in X1 is associated with a 0.65 standard deviation in Y, controlling for the effect of X2. 
B)  A one unit change in X1 is associated with a 0.65 standard deviation in X2, controlling for the effect of Y. 
C)  A one standard deviation change in X2 is associated with a 0.65 standard deviation change in Y, controlling for the effect of X1. 
D)  There is an error in this equation: beta-weights for X1 and X2 cannot have opposite signs.

Question 10

Where would a researcher look for guidance in determining what variables to control for?

Accepted Answer

A)  in the theory 
B)  in a good statistics text 
C)  in the research design 
D)  in the equations 
A)  in the theory 
B)  in a good statistics text 
C)  in the research design 
D)  in the equations

Question 11

Suppose the effect of testosterone on aggression differs according to a third variable, age. What is the problem with this scenario in multiple regression analysis?

Accepted Answer

A)  The independent variables have an interactive relationship. 
B)  The independent variables have additive effects. 
C)  The independent variables are heteroskedastic. 
D)  The independent variables are uncorrelated with one another. 
A)  The independent variables have an interactive relationship. 
B)  The independent variables have additive effects. 
C)  The independent variables are heteroskedastic. 
D)  The independent variables are uncorrelated with one another.

Question 12

Beta weights are dependent on what type of statistical transformation?

Accepted Answer

A)  conversion of simple slopes into partial slopes 
B)  conversion of raw scores into Z scores 
C)  conversion of coefficients of determination into coefficients of multiple determination 
D)  conversion of Y intercepts into partial slopes 
A)  conversion of simple slopes into partial slopes 
B)  conversion of raw scores into Z scores 
C)  conversion of coefficients of determination into coefficients of multiple determination 
D)  conversion of Y intercepts into partial slopes

Question 13

What is revealed by the unstandardized partial slopes in the least-squares multiple regression equation?

Accepted Answer

A)  the point where the line crosses the Y axis 
B)  the combined effects of all independents on the dependent variable 
C)  the amount of change in Y for a unit change in one independent variable while controlling for all other independent variables 
D)  the residual effects of the independent after partialling out the effect of the dependent variable 
A)  the point where the line crosses the Y axis 
B)  the combined effects of all independents on the dependent variable 
C)  the amount of change in Y for a unit change in one independent variable while controlling for all other independent variables 
D)  the residual effects of the independent after partialling out the effect of the dependent variable

Question 14

What is a partial correlation used for?

Accepted Answer

A)  to investigate the mutual effects of two variables on each other 
B)  to investigate what happens when many variables are free to vary 
C)  to investigate how a specific bivariate relationship is affected by a control variable 
D)  to investigate what happens to the third variable when the first two are controlled 
A)  to investigate the mutual effects of two variables on each other 
B)  to investigate what happens when many variables are free to vary 
C)  to investigate how a specific bivariate relationship is affected by a control variable 
D)  to investigate what happens to the third variable when the first two are controlled

Question 15

Suppose that, in a multiple regression equation, a = 5, b1 = 1, b2 = 15, X1 = 5, and X2 = 4. What is the predicted Y score?

Accepted Answer

A)  20 
B)  30 
C)  40 
D)  70 
A)  20 
B)  30 
C)  40 
D)  70

Question 16

Suppose there is a positive bivariate relationship between pathogen exposure and blood pressure. Which of these scenarios would most clearly reveal this as a spurious association?

Accepted Answer

A)  Occupational prestige caused both pathogen exposure and blood pressure. 
B)  Pathogen exposure decreases immune functioning, which raises blood pressure. 
C)  The association between pathogen exposure and blood pressure is actually non-linear. 
D)  Pathogen exposure has a stronger relationship with blood pressure among men than it does among women. 
A)  Occupational prestige caused both pathogen exposure and blood pressure. 
B)  Pathogen exposure decreases immune functioning, which raises blood pressure. 
C)  The association between pathogen exposure and blood pressure is actually non-linear. 
D)  Pathogen exposure has a stronger relationship with blood pressure among men than it does among women.

Question 17

When will the coefficient of determination decrease when a second independent variable is added alongside the initial independent variable in a regression analysis?

Accepted Answer

A)  when X2 predicts less variation in Y than does X1 
B)  when X1 predicts less variation in Y than does X2 
C)  when the partial slopes are drastically different from one another 
D)  It will not decrease; the coefficient of determination with two variables represents variation explained by X2 after X1 has been accounted for, which cannot be less than the initial r2 value. 
A)  when X2 predicts less variation in Y than does X1 
B)  when X1 predicts less variation in Y than does X2 
C)  when the partial slopes are drastically different from one another 
D)  It will not decrease; the coefficient of determination with two variables represents variation explained by X2 after X1 has been accounted for, which cannot be less than the initial r2 value.

Question 18

Which of these statements best describes the requirements of independent variables in multiple regression?

Accepted Answer

A)  All X variables must be strongly correlated with each other. 
B)  At least one X variable will have linear associations with Y; the Y variable is nominal or ordinal. 
C)  All X variables have additive and linear association with Y. 
D)  There can be no more than four X variables; there can be only low correlation between them. 
A)  All X variables must be strongly correlated with each other. 
B)  At least one X variable will have linear associations with Y; the Y variable is nominal or ordinal. 
C)  All X variables have additive and linear association with Y. 
D)  There can be no more than four X variables; there can be only low correlation between them.

Question 19

The coefficient of determination (r2) for a regression equation with one independent variable (X1) is 0.63. A second independent variable (X2) is added to the equation, and the coefficient of determination changes to 0.64. Which of the following would we conclude?

Accepted Answer

A)  Together, X1 and X2 explain only about 40% of the variability in the dependent variable. 
B)  X2 contributes little over and above the effect of X1 to our ability to understand variability in the dependent variable. 
C)  Adding X2 increases our ability to understand variability in the dependent variable by a considerable margin. 
D)  X2 intervenes between X1 and the dependent variable. 
A)  Together, X1 and X2 explain only about 40% of the variability in the dependent variable. 
B)  X2 contributes little over and above the effect of X1 to our ability to understand variability in the dependent variable. 
C)  Adding X2 increases our ability to understand variability in the dependent variable by a considerable margin. 
D)  X2 intervenes between X1 and the dependent variable.

Question 20

A zero-order correlation for a bivariate association is -0.65. After controlling for Z, we again observe a partial correlation of -0.65. Which of the following is the best interpretation of this finding?

Accepted Answer

A)  The relationship between X and Y is clearly spurious or association. 
B)  There is no evidence that Z makes the relationship between X and Y spurious. 
C)  There is no association between X and Y. 
D)  There is an interactive association between X and Y. 
A)  The relationship between X and Y is clearly spurious or association. 
B)  There is no evidence that Z makes the relationship between X and Y spurious. 
C)  There is no association between X and Y. 
D)  There is an interactive association between X and Y.

What is the relationship between a first-order and a zero-order correlation?

Which of the following is the value of a (the Y intercept) after scores have been standardized?

Why is comparison of the separate effects of multiple independent variables often a challenge in multiple regression?

In which of these scenarios would a standardized multiple regression equation be least useful?

X has a causal influence on Y, even after Z is controlled. What is the term for this relationship between X and Y?

Consider a multiple regression equation predicting life expectancy in a random sample of 35 countries. X₁ is per capita GDP and X₂ is the country's homicide rate (per 100,000). Suppose the regression equation is Y = a + 0.5(X₁) - 0.08(X₂). How should we interpret a?

How many variables can be used in a multiple regression equation?

In this least-squares regression equation, Y = a + b₁X₁ + b₂X₂, what represents the partial slopes?

A standardized multiple regression equation yields a beta weight of 0.65 for X₁ and -0.50 for X₂. Which of the following is an interpretation of X₁'s beta weight?

Where would a researcher look for guidance in determining what variables to control for?

Suppose the effect of testosterone on aggression differs according to a third variable, age. What is the problem with this scenario in multiple regression analysis?

Beta weights are dependent on what type of statistical transformation?

What is revealed by the unstandardized partial slopes in the least-squares multiple regression equation?

What is a partial correlation used for?

Suppose that, in a multiple regression equation, a = 5, b₁ = 1, b₂ = 15, X₁ = 5, and X₂ = 4. What is the predicted Y score?

Suppose there is a positive bivariate relationship between pathogen exposure and blood pressure. Which of these scenarios would most clearly reveal this as a spurious association?

When will the coefficient of determination decrease when a second independent variable is added alongside the initial independent variable in a regression analysis?

Which of these statements best describes the requirements of independent variables in multiple regression?

The coefficient of determination (r²) for a regression equation with one independent variable (X₁) is 0.63. A second independent variable (X₂) is added to the equation, and the coefficient of determination changes to 0.64. Which of the following would we conclude?

A zero-order correlation for a bivariate association is -0.65. After controlling for Z, we again observe a partial correlation of -0.65. Which of the following is the best interpretation of this finding?

Introduction

Basic Descriptive Statistics: Percentages, Ratios and Rates, Tables, Charts, and Graphs

Measures of Central Tendency and Dispersion

The Normal Curve

Introduction to Inferential Statistics: Sampling and the Sampling Distribution

Estimation Procedures for Sample Means and Proportions

Hypothesis Testing With Nominal and Ordinal Variables: CHI Square

Measures of Association for Variables Measured at the Nominal Level

Measures of Association for Variables Measured at the Ordinal Level

Hypothesis Testing With Means and Proportions: The One-Sample Case

Hypothesis Testing With Means and Proportions: The Two-Sample Case

Hypothesis Testing With More Than Two Means: One-Way Analysis of Variance

Hypothesis Testing and Measures of Association for Variables Measured at the Interval-Ratio Level

Filters

Exam 14: Partial Correlation and Multiple Regression and Correlation

What is the relationship between a first-order and a zero-order correlation?

Which of the following is the value of a (the Y intercept) after scores have been standardized?

Why is comparison of the separate effects of multiple independent variables often a challenge in multiple regression?

In which of these scenarios would a standardized multiple regression equation be least useful?

X has a causal influence on Y, even after Z is controlled. What is the term for this relationship between X and Y?

Consider a multiple regression equation predicting life expectancy in a random sample of 35 countries. X1 is per capita GDP and X2 is the country's homicide rate (per 100,000). Suppose the regression equation is Y = a + 0.5(X1) - 0.08(X2). How should we interpret a?

How many variables can be used in a multiple regression equation?

In this least-squares regression equation, Y = a + b1X1 + b2X2, what represents the partial slopes?

A standardized multiple regression equation yields a beta weight of 0.65 for X1 and -0.50 for X2. Which of the following is an interpretation of X1's beta weight?

Where would a researcher look for guidance in determining what variables to control for?

Suppose the effect of testosterone on aggression differs according to a third variable, age. What is the problem with this scenario in multiple regression analysis?

Beta weights are dependent on what type of statistical transformation?

What is revealed by the unstandardized partial slopes in the least-squares multiple regression equation?

What is a partial correlation used for?

Suppose that, in a multiple regression equation, a = 5, b1 = 1, b2 = 15, X1 = 5, and X2 = 4. What is the predicted Y score?

Suppose there is a positive bivariate relationship between pathogen exposure and blood pressure. Which of these scenarios would most clearly reveal this as a spurious association?

When will the coefficient of determination decrease when a second independent variable is added alongside the initial independent variable in a regression analysis?

Which of these statements best describes the requirements of independent variables in multiple regression?

The coefficient of determination (r2) for a regression equation with one independent variable (X1) is 0.63. A second independent variable (X2) is added to the equation, and the coefficient of determination changes to 0.64. Which of the following would we conclude?

A zero-order correlation for a bivariate association is -0.65. After controlling for Z, we again observe a partial correlation of -0.65. Which of the following is the best interpretation of this finding?

Introduction

Basic Descriptive Statistics: Percentages, Ratios and Rates, Tables, Charts, and Graphs

Measures of Central Tendency and Dispersion

The Normal Curve

Introduction to Inferential Statistics: Sampling and the Sampling Distribution

Estimation Procedures for Sample Means and Proportions

Hypothesis Testing With Nominal and Ordinal Variables: CHI Square

Measures of Association for Variables Measured at the Nominal Level

Measures of Association for Variables Measured at the Ordinal Level

Hypothesis Testing With Means and Proportions: The One-Sample Case

Hypothesis Testing With Means and Proportions: The Two-Sample Case

Hypothesis Testing With More Than Two Means: One-Way Analysis of Variance

Hypothesis Testing and Measures of Association for Variables Measured at the Interval-Ratio Level

Filters

Consider a multiple regression equation predicting life expectancy in a random sample of 35 countries. X₁ is per capita GDP and X₂ is the country's homicide rate (per 100,000). Suppose the regression equation is Y = a + 0.5(X₁) - 0.08(X₂). How should we interpret a?

In this least-squares regression equation, Y = a + b₁X₁ + b₂X₂, what represents the partial slopes?

A standardized multiple regression equation yields a beta weight of 0.65 for X₁ and -0.50 for X₂. Which of the following is an interpretation of X₁'s beta weight?

Suppose that, in a multiple regression equation, a = 5, b₁ = 1, b₂ = 15, X₁ = 5, and X₂ = 4. What is the predicted Y score?

The coefficient of determination (r²) for a regression equation with one independent variable (X₁) is 0.63. A second independent variable (X₂) is added to the equation, and the coefficient of determination changes to 0.64. Which of the following would we conclude?