Question 1

What is a partial correlation used for?
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

Accepted Answer

Partial correlation is used to measure the strength and direction of a relationship between two variables while controlling for the effect of one or more additional variables.

Question 2

What types of data are required for partial and multiple correlation and regression?
A) nominal and continuous
B) inferential and bivariate
C) interval-ratio
D) ordinal and discrete

Accepted Answer

Partial and multiple correlation and regression require interval-ratio data, which are continuous and allow for meaningful comparison of differences and ratios.

Question 3

Researchers determine that age has a positive correlation with trust of one's neighbours. They then ask whether this correlation is due to the fact that older people tend to have lived for longer amounts of time in their neighbourhood relative to younger people. What type of variable is "time lived in neighbourhood" for this example?
A) a beta variable
B) a zero-order variable
C) a dependent variable
D) a control variable

Accepted Answer

"Time lived in neighbourhood" is a control variable because researchers are considering it to see if it explains the correlation between age and trust of one's neighbours.

Question 4

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

Accepted Answer

The first-order correlation adjusts the zero-order correlation by controlling for the influence of a third variable, providing a more refined understanding of the relationship between the primary variables.

Question 5

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?
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.

Accepted Answer

The partial correlation remaining the same after controlling for Z suggests that Z does not influence the relationship between X and Y, indicating no evidence of a spurious relationship.

Question 6

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?
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.

Accepted Answer

A spurious association occurs when two variables are correlated but not causally related, often due to a third variable causing both. In this case, if occupational prestige causes both pathogen exposure and blood pressure, it would reveal the association as spurious.

Question 7

X has a causal influence on Y, even after Z is controlled. What is the term for this relationship between X and Y?
A) partial correlation relationship
B) direct relationship
C) spurious relationship
D) intervening relationship

Accepted Answer

A direct relationship implies that X influences Y directly, even when other variables like Z are controlled for.

Question 8

Which of the following best describes an intervening relationship between the variables "literacy," "economic productivity," and "wealth" for a sample of countries?
A) Literacy increases wealth, no matter the value of economic productivity.
B) Literacy increases economic productivity, which increases wealth.
C) Wealth is caused by neither literacy nor economic productivity.
D) Economic productivity increases wealth only when there are high levels of literacy.

Accepted Answer

Literacy can enhance economic productivity by providing individuals with the skills needed for more efficient work, which in turn can lead to increased wealth.

Question 9

The correlation in a large company between self-confidence and income is 0.25. After controlling for level of authority on the job, the original correlation dips to 0.11. What is this evidence of?
A) a direct relationship between self-confidence and income
B) a spurious relationship between self-confidence and income; job authority causes both
C) an intervening relationship between self-confidence and income; self-confidence affects income through increasing people's job authority
D) either a spurious or an intervening relationship; it is impossible to differentiate the two possibilities on statistical grounds

Accepted Answer

The answer of The correlation in a large company between...

Question 10

Where would a researcher look for guidance in determining what variables to control for?
A) in the theory
B) in a good statistics text
C) in the research design
D) in the equations

Accepted Answer

Researchers should look to the theory related to their study to determine which variables are relevant and should be controlled for, as the theory provides the framework and context for understanding the relationships between variables.

Question 11

A theory suggests that X should have a positive effect on Y. Upon analyzing a set of data, the correlation between X and Y is 0.55, and remains just as strong when Z is controlled. What does this tell us about the theory in question?
A) The theory was on the right track, but had the direction of the effect reversed.
B) The theory is proven correct.
C) The theory is supported, but other control variables need to be considered.
D) Nothing can be learned about the theory.

Accepted Answer

The positive correlation of 0.55 supports the theory that X has a positive effect on Y. The fact that this correlation remains strong when controlling for Z suggests that Z does not confound the relationship, but other variables might still need to be considered to fully validate the theory.

Question 12

In this least-squares regression equation, Y = a + b₁X₁ + b₂X₂, what represents the partial slopes? A) y and a B) the sum of b₁X₁ and b₂X₂ C) the xs D) the bs

Accepted Answer

The partial slopes in a regression equation are represented by the coefficients b₁ and b₂, which indicate the change in Y for a one-unit change in X₁ or X₂, holding other variables constant.

Question 13

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

Accepted Answer

In multiple regression, any number of independent variables can be used to predict the dependent variable, as long as the model is statistically valid and the data supports it.

Question 14

How should the symbol b be interpreted in a multiple regression equation? A) as the value of Y when all independent variables have a score of 0 B) as the amount of Y for a unit change in the independent variable while controlling for the effects of all other variables C) as the correlation between two independent variables D) as the effect of X₁ on X₂ while controlling for the effect of Y

Accepted Answer

In a multiple regression equation, the symbol b represents the coefficient for an independent variable, indicating the amount of change in the dependent variable Y for a one-unit change in that independent variable, while holding all other variables constant.

Question 15

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

Accepted Answer

The unstandardized partial slopes in a multiple regression equation indicate the change in the dependent variable (Y) for a one-unit change in an independent variable, while holding all other independent variables constant.

Question 16

Suppose that, in a multiple regression equation, a = 5, b₁ = 1, b₂ = 15, X₁ = 5, and X₂ = 4. What is the predicted Y score? A) 20 B) 30 C) 40 D) 70

Accepted Answer

The answer of Suppose that, in a multiple regression equation,...

Question 17

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? 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.

Accepted Answer

It is the predicted life expectancy value when a country has a GDP of 0 and a homicide rate of 0.

Question 18

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

Accepted Answer

Different independent variables often have different units of measurement, which can make it challenging to directly compare their effects in a multiple regression model.

Question 19

Beta weights are dependent on what type of statistical transformation?
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

Accepted Answer

Beta weights are standardized coefficients that result from converting raw scores into Z scores, allowing for comparison across different variables.

Question 20

What is the major advantage of a standardized multiple regression equation?
A) a simple comparison of each variable's relative importance
B) predicting values of the dependent variable (  ) in the variable's original units
C) the ability to incorporate multiple independent variables; the bivariate nature of unstandardized regression
D) assessing non-linear associations between independent and dependent variables

Accepted Answer

The answer of What is the major advantage of a...

Quiz 14: Partial Correlation and Multiple Regression and Correlation

What is a partial correlation used for?

What types of data are required for partial and multiple correlation and regression?

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

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?

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?

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

Which of the following best describes an intervening relationship between the variables "literacy," "economic productivity," and "wealth" for a sample of countries?

The correlation in a large company between self-confidence and income is 0.25. After controlling for level of authority on the job, the original correlation dips to 0.11. What is this evidence of?

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

A theory suggests that X should have a positive effect on Y. Upon analyzing a set of data, the correlation between X and Y is 0.55, and remains just as strong when Z is controlled. What does this tell us about the theory in question?

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

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

How should the symbol b be interpreted in a multiple regression equation?

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

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

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?

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

Beta weights are dependent on what type of statistical transformation?

What is the major advantage of a standardized multiple regression equation?