Deck 17: Partial Correlation and Multiple Regression and Correlation

Question 1

For multivariate analysis,the techniques of partial correlation and multiple regression and correlation are superior to elaboration (i.e. ,controlling for a third variable by constructing partial tables)because

A)computations are easier.
B)they avoid the necessity of computing Pearson's r.
C)they provide less information and are less confusing.
D)they provide more information.

Answer 1

they provide more information.

Question 2

A Pearson's r calculated for the bivariate relationship between X and Y is .50.After controlling for Z,the partial correlation coefficient is .49.This outcome would be evidence of a(n)____ relationship between X and Y.

A)direct
B)spurious
C)interactive
D)negative

Answer 2

direct

Question 3

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

Answer 3

spurious or intervening

Question 4

After controlling for Z,a researcher finds evidence of a direct 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 5

A researcher examines the relationship between poverty and crime rates for 100 metropolitan areas and finds a zero-order correlation of 0.37.She controls for the percent of families that are headed by single parents and finds a first order partial correlation of 0.33.This is a ____ relationship.

A)direct
B)statistically significant
C)spurious
D)interactive

Question 6

Partial and multiple correlation require data which are

A)nominal and continuous.
B)ordinal and discrete.
C)inferential and bivariate.
D)interval-ratio.

Question 7

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 8

After controlling for Z,the partial correlation coefficient is .78.The bivariate Pearson's r between X and Y was only .51.Which interpretation is consistent with these results?

A)None,these results are mathematically impossible.
B)There is a spurious relationship between X and Y.
C)X and Z are both caused by Y.
D)X and Z are separate,uncorrelated causes of Y.

Question 9

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 10

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

A)the partial correlation coefficients 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 above.Partial correlation will not detect interaction.

Question 11

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 12

If the variables of interest do not meet the level of measurement requirements of partial and multiple correlation,an alternative statistical technique that would produce analogous information would be

A)Pearson's r.
B)elaborating bivariate tables.
C)chi square.
D)gamma and phi.

Question 13

Partial correlation will detect all of the following relationships among variables except

A)interaction.
B)direct relationships.
C)spurious relationships.
D)intervening relationships.

Question 14

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.

Question 15

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 16

Partial correlation is analogous to

A)elaborating bivariate tables.
B)finding the regression equation.
C)computing chi square.
D)controlling for the dependent variable.

Question 17

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 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

Partial and multiple correlation are based on

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

Question 20

A researcher examines the relationship between poverty and crime rates for 100 metropolitan areas and finds a zero-order correlation of 0.37.She controls for the percent of families that are headed by single parents and finds a first order partial correlation of 0.06.This is a ____ relationship.

A)direct
B)statistically significant
C)spurious
D)interactive

Question 21

If a = 17,b₁ = 5,b₂ = 20,X₁= 100,and X₂ = 200,what would the predicted Y score be?

A)17
B)4,517
C)101
D)6,217

Question 22

In regression analysis,the standardized partial slopes are symbolized as

A)b*
B)B
C)b^#
D)r*

Question 23

Standardized partial slopes are also called

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

Question 24

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

A)Y = a + bX₂.
B)Y = a + b + X₁ + X₂.
C)Y = b₁X₁ + b₂X_2.
D)Y = a + b₁X₁ + b₂X_2.

Question 25

A researcher wants to predict score on personal happiness (Y)from score on income (X₁)and number of friends (X₂).Which of the following would be the proper course of action?

A)use the standardized partial slopes of X₁ and X₂ on Y
B)examine the unstandardized partial slopes of X₁ and X₂ on Y
C)compute the partial correlation coefficient for X₁ and X₂ controlling for Y
D)examine the partial slope of Y on each independent separately

Question 26

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 27

In the multiple regression equation,the symbol b stands for

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

Question 28

To investigate the combined effects of several independent variables on a single dependent variable,we use

A)partial correlation and regression.
B)bivariate correlation and regression.
C)multiple correlation and regression.
D)interactive correlation and regression.

Question 29

A researcher is trying to determine if income (X₁)or number of friends (X₂)is more important in determining personal happiness (Y).Which of the following would be the most profitable course of action?

A)examine the standardized partial slopes of X₁ and X₂ on Y
B)examine the unstandardized partial slopes of X₁ and X₂ on Y
C)compute the partial correlation coefficient for X₁ and X₂ controlling for Y
D)examine the partial slope of Y on each independent separately

Question 30

If a = 1,b₁ = 10,b₂ = 10,X₁= 2,and X₂ = 3,what would the predicted Y score be?

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

Question 31

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

Question 32

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

A)Zy = a - b₁*Z₁ - b₂Z₂
B)Zy = a + b₁X₁ - b₂X₂
C)Zy = b₁*Z₁ + b₂*Z₂
D)Zy = b₁*Z₁ - b₂Z₂

Question 33

The regression equation for a particular relationship is Y = 10 + (.78)X₁ + (-.54)X₂.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 34

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 35

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

A)1.
B)0.
C)b₁ - b_2.
D)R².

Question 36

In the multiple regression equation,the partial slopes are represented by the symbol

A)a
B)b*
C)a*
D)b

Question 37

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 38

After controlling for Z,the partial correlation coefficient is .78.The bivariate Pearson's r between X and Y was only .51.What should the researcher do next?

A)Use multiple regression techniques to investigate this relationship further.
B)Halt the investigation since these results are mathematically impossible.
C)Conclude that the relationship between Z and Y is direct.
D)Conclude that the relationship between Z and Y is spurious.

Question 39

In the multiple regression equation,the partial slopes are analogous to

A)chi square.
B)gamma.
C)Pearson's r.
D)the partial correlation coefficient.

Question 40

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 41

A researcher is examining the effects of income (X₁)and number of friends (X₂)on personal happiness (Y)and finds an R² 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 42

The multiple regression analysis of the relationship between crime and poverty used a dummy variables based on

A)region.
B)gender.
C)race.
D)religion.

Question 43

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 44

Under what condition could the coefficient of multiple determination (R²)be lower in value than the zero-order correlation coefficients?

A)under no condition.This is mathematically impossible.
B)only when all bivariate relationships are negative
C)only when all bivariate relationships are zero
D)only when the relationships are spurious

Question 45

A standardized regression equation is stated as: Zy = (.46)Z₁ + (.47)Z₁.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 46

If the beta-weight of the first independent (X₁)is .45 and the beta-weight of the second independent (X₂)is -.50,then

A)X₁ has a stronger direct effect than X_2.
B)X₂ has a stronger direct effect than X_1.
C)Y₂ must equal zero.
D)the multiple correlation coefficient must be negative.

Question 47

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 48

The techniques of multiple correlation and regression can be used

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

Question 49

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

A)the amount of variation explained by X₁ plus the amount of variation explained by X₂ after controlling for the effect of X_1.
B)the amount of variation explained by X₁ minus the amount of variation unexplained by X_2.
C)the total variation in Y minus the amount unexplained by X₁ after controlling for X_2.
D)the sum of all explained and unexplained variation in X₁ and X_2.

Question 50

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 51

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 52

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 53

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.