Deck 14: Partial Correlation and Multiple Regression and Correlation

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

Answer 1

to investigate how a specific bivariate relationship is affected by a control variable

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

Answer 2

interval-ratio

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

Answer 3

a control variable

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.

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.

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.

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

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.

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

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

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.

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

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.

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

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

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

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.

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.

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

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

Question 21

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

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 22

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?

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 23

Which of the following is a standardized multiple regression equation with two independent variables?

A) Z_y = a - b₁Z₁ - b₂Z₂
B) Z_y = b₁Z₁ + b₂Z₂
C) Z_y = b₁Z₁ - b₂Z₂
D) Z_y = a + b₁X₁ + b₂X₂

Question 24

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

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

Question 25

A standardized regression equation is stated as
. Which of these conclusions is consistent with this formula?

A) Z is caused by both X and Y.
B) There is a direct relationship between X and Y after controlling for the effects of Z.
C) The independent variables have strong, nearly equal relationships with the dependent variable.
D) This is a spurious relationship.

Question 26

A standardized regression equation with Olympic athletes' sprint times as the dependent variable features two X variables. The beta-weight for sprinters' height (X₁) is -0.18, and the beta-weight for sprinters' weight (X₂) is 0.26. Which of the following can we conclude from these results?

A) Weight has a stronger effect than height on race times.
B) Height has a stronger effect than weight on race times.
C) The coefficient of determination is 0.08.
D) The coefficient of determination is 0.44.

Question 27

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

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 28

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) 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 29

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

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 30

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?

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 31

Consider the multiple regression equation Y = a + b₁X₁ + b₂X₂. What is the ideal correlation between X₁ and X₂, assuming the assumptions of multiple regression are fully met?

A) r = 0
B) r = 0.5
C) r = 1
D) r = 2

Question 32

Briefly explain the difference between additive and interactive effects of independent variables in multiple regression.