Deck 15: Partial Correlation and Multiple Regression and Correlation

Question 1

With two independent variables, the least-squares multiple regression equation would be________.

A) Y = a + bX
B) Y = a + b + X 1 + X²
C) Y = b 1 X 1 + b 2 X 2
D) Y = a + b 1 X 1 + b 2 X 2

Answer 1

D

Question 2

One advantage of the technique of multiple regression is that it allows the ___________ effects of the ____________ variables to be investigated.

A) combined, independent
B) separate, independent
C) combined, control
D) separate, dependent

Answer 2

B

Question 3

After controlling for Z, the partial correlation coefficient between X and Y is the same value as the bivariate Pearson's r. This pattern would be taken as evidence of________.

A) a direct relationship between X and Y.
B) a spurious relationship between X and Z.
C) interaction between X, Y, and Z.
D) an intervening relationship between X and Y, interaction between X and Z.

Answer 3

A

Question 4

Standardized partial slopes are also called________.

A) alpha levels.
B) gammas.
C) Z scores.
D) beta-weights.

Question 5

In the multiple regression equation, the symbol b stands for the________.

A) partial slope.
B) slope of X and Y.
C) beta slope of X and Z.
D) Y intercept.

Question 6

The regression equation for a particular relationship is Y = 10 + (.78) X 1+ (-.54) X 2. Which conclusion is consistent with this equation?

A) The Y intercept is zero.
B) Neither independent variable has an important relationship with Y.
C) A value for a (the Y intercept) needs to be calculated before the equation can be interpreted.
D) The two independent variables have opposite effects on the dependent.

Question 7

If a = 1, b 1= 10, b 2= 10, X 1= 2, and X 2= 3, what would the predicted Y score be?

A) 51
B) 26
C) 5
D) 0

Question 8

After scores have been standardized, the value of a (the Y-intercept) will always be________.

A) 1
B) 0
C) b1 - b2
D) R 2

Question 9

When examining a bivariate relationship using Pearson's r, the partial correlation computed while using one control variable is called________.

A) the first-order partial correlation coefficient.
B) the second-order partial correlation coefficient.
C) the intervening partial correlation coefficient.
D) the multiple partial correlation coefficient.

Question 10

If the beta-weight of the first independent (X 1) is .45 and the beta-weight of the second independent (X 2) is -.50, then________.

A) X 1 has a stronger direct effect than X 2.
B) X 2 has a stronger direct effect than X 1.
C) Y 2 must equal zero.
D) the multiple correlation coefficient must be negative.

Question 11

In the least-squares multiple regression equation, the unstandardized partial slopes show________.

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 12

Partial and multiple correlation are based on________.

A) bivariate tables.
B) random sampling.
C) the Analysis of Variance.
D) Pearson's r.

Question 13

The coefficient of multiple determination (R2) shows________.

A) the effect of the control variable after removing the independent from the equation.
B) essentially the same thing as a partial gamma.
C) the combined effects of all independents on the dependent.
D) the zero-order relationships after controlling for the independents.

Question 14

While unstandardized partial slopes permit predictions of Y in the original units of the variable, standardized partial slopes permit an assessment of________.

A) the combined effects of the independents.
B) the partial effects of the independents.
C) the independent effects of the partials.
D) the relative importance of the independents.

Question 15

Which of the following is a correctly stated standardized regression equation?

A) Zy = a - b 1 *Z 1 - b 2 Z 2
B) Zy = a + b 1 X 1 - b 2 X 2
C) Zy = b 1 *Z 1 + b 2 *Z 2
D) Zy = b 1 *Z 1 - b 2 Z 2

Question 16

If a researcher wants to predict the value of a dependent variable based upon known independent variables for a specific case, they would use________.

A) standardized partial slopes.
B) correlations.
C) unstandardized partial slopes.
D) none of these choices are correct.

Question 17

Standardized partial slopes can be computed by________.

A) converting all scores to Z scores.
B) converting all scores to percentages.
C) converting the partial slopes to Z scores.
D) taking a percentage of the partial slopes.

Question 18

The 'first-order' partial correlation coefficient measures________.

A) the bivariate relationship between X and Y.
B) the relationship between the dependent and control variables.
C) the bivariate relationship after controlling for the third variable.
D) the bivariate relationship after controlling for the fourth variable.

Question 19

A standardized regression equation is stated as: Zy = (.46)Z 1+ (.47)Z 1. Which conclusion is most consistent with this formula?

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

Question 20

In an equation where the beta-weight for poverty is 0.73 and for age is -0.13, what would be the intercept in the standardized least-squares regression line?

A) 0
B) 0.60
C) 0.86
D) cannot determine from this information.

Question 21

Which of the following is not a prerequisite for the use of the techniques of multiple regression and correlation?

A) interval-ratio level of measurement
B) linear relationships
C) no interaction among the variables
D) partial slopes less than zero

Question 22

Which of the following would be consistent with a spurious relationship between X and Y?

A) Pearson's r is .37, partial correlation coefficient is .36.
B) Pearson's r is .78, partial correlation coefficient is .30.
C) Pearson's r is -.10, partial correlation coefficient is -.15.
D) Pearson's r is .00, partial correlation coefficient is .00.

Question 23

After controlling for Z, a researcher finds evidence of a spurious relationship between X and Y. What step should be taken next?

A) Z should become the new independent variable.
B) Z should become the new dependent variable.
C) Z should be disregarded and a new control variable should be selected.
D) Z should be disregarded and a new independent variable should be selected.

Question 24

In the analysis of the relationship between crime, poverty, age, and region reported in the text, which independent variable(s) had the strongest effect on the dependent variable according to the beta-weights?

A) Region
B) Poverty and age had equally strong effects
C) Region and age had equally strong effects
D) Poverty

Question 25

The partial correlation coefficient will reveal an interactive relationship between three variables when________.

A) the partial correlation coefficient drops to zero.
B) the partial is greater in value than the zero-order correlation coefficient.
C) the partial correlation coefficient is negative.
D) none of the answer choices. Partial correlation will not detect interaction.

Question 26

An analysis of the relationship between income and education found a correlation of 0.43. After controlling for age, the partial correlation was 0.43. The relationship between income and education seems to be________.

A) direct.
B) spurious.
C) intervening.
D) interactive.

Question 27

A Pearson's r calculated for a bivariate relationship is .50. After controlling for Z, the partial correlation coefficient is .07. This outcome would be evidence of a(n) _____________ relationship between X and Y.

A) direct
B) spurious or intervening
C) interactive
D) positive

Question 28

The partial correlation coefficient between X and Y after controlling for Z shows a much weaker relationship than the Pearson's r computed for X and Y. This would be taken as evidence of a(n) _____________ relationship between X and Y.

A) direct
B) spurious or intervening
C) interactive
D) positive

Question 29

To the extent that the variables do not meet the assumptions of regression analysis, coefficients and slopes become________.

A) greater in value.
B) lower in value.
C) less trustworthy.
D) less representative of the population.

Question 30

A researcher is examining the effects of income (X 1) and number of friends (X 2) on personal happiness (Y) and finds an R of 0.45. Which of the following is a correct interpretation of this result?

A) Money CAN buy happiness.
B) Friends are more important than money for happiness.
C) Taken together, income and number of friends explain 45% of the variance in happiness.
D) Taken together, income and number of friends explain 0.45% of the variance in happiness.

Question 31

Which of the following would be consistent with a causal model in which X and Z had independent and uncorrelated causal effects on Y?

A) Pearson's r is .37, partial correlation coefficient is .36.
B) Pearson's r is .30, partial correlation coefficient is .50.
C) Pearson's r is -.10, partial correlation coefficient is -.01.
D) Pearson's r is -.41 partial correlation coefficient is .00.

Question 32

The coefficient of multiple determination (R2), with two independent variables is________.

A) the amount of variation explained by X 1 plus the amount of variation explained by X 2, after controlling for the effect of X 1 .
B) the amount of variation explained by X 1 minus the amount of variation unexplained by X 2 .
C) the total variation in Y minus the amount unexplained by X 1 after controlling for X 2 .
D) the sum of all explained and unexplained variation in X 1 and X 2.

Question 33

Which of the following would be consistent with a direct relationship between X and Y?

A) Pearson's r is .17, partial correlation coefficient is .16.
B) Pearson's r is .78, partial correlation coefficient is .50.
C) Pearson's r is .10, partial correlation coefficient is .20.
D) Pearson's r is .00, partial correlation coefficient is .00.

Question 34

The text presents information from a research project on the relationships between crime, poverty, and age. After controlling for age, the relationship between crime and poverty was found to be________.

A) spurious.
B) direct.
C) interactive.
D) intervening.

Question 35

The techniques of multiple correlation and regression can be used as long as________.

A) the total number of variables is not greater than three.
B) the independents are strongly correlated with each other.
C) each independent is linearly related with the dependent variable.
D) sample size is less than 100.

Question 36

It is possible that a published journal article would include ______ in their analysis of a multiple regression model.

A) a standardized coefficient
B) an unstandardized coefficient
C) R 2
D) all of these choices are correct.

Question 37

The auto theft rate (number of auto thefts known to the police per 100,000 population), unemployment rate, and percent of the population consisting of adolescent and young adult males (ages 12 - 25) are presented below for a sample of twenty cities. Take auto theft rate as the dependent variable and conduct a full regression analysis for these three variables.