Deck 13: Controlling for a Third Variable: Multiple OlS Regression

Question 1

Which of the following is NOT one of the things that need to exist before we conclude that a causal connection exists between two variables?

A) nonspuriousness
B) correlation
C) temporal order
D) multicollinearity

Answer 1

D

Question 2

Spuriousness occurs when ______.

A) a third variable causes both the independent and dependent variable
B) a third variable causes the dependent variable only
C) a third variable causes the independent variable only
D) a third is caused by both the independent and dependent variables

Answer 2

A

Question 3

In a study, researchers find that ice cream consumption predicts increased crime. However, once they control for summertime (which also predicts crime), the relationship goes away. This is an example of ______.

A) nonspuriousness
B) temporal order
C) correlation
D) spuriousness

Answer 3

D

Question 4

Which of the following is NOT an assumption of the multivariate regression model?

A) The dependent variable is measured at the interval/ratio level.
B) The relationship between the independent and dependent variables is linear.
C) The independent variables are not highly correlated among themselves.
D) The error term is correlated with each of the independent variables.

Question 5

A partial slope coefficient is ______.

A) the effect of the independent variable on the dependent variable
B) the effect of the independent variable on the dependent variable after controlling for other independent variables
C) the partial effect of the independent variable on the dependent variable
D) the effect of the dependent variable on the independent variable

Question 6

When the independent variables are too highly correlated in a regression equation, they are considered to be?

A) partial coefficients
B) spurious
C) inter-leveraging
D) multicollinear

Question 7

Why is multicollinearity a problem?

A) It induces a spurious relationship between the independent variables and the dependent variables.
B) It is difficult to identify which of the collinear variables are influencing the dependent variable.
C) It increases type I error.
D) It reduces the standard errors.

Question 8

One remedy for multicollinearity is to ______.

A) remove all of the troublesome variables
B) increase the sample size
C) remove one of the troublesome variables and re-estimate the equation
D) obtain the partial slope coefficient

Question 9

Given a multiple regression model with four independent variables, which of the following standardized partial slopes would have the strongest relationship with the dependent variable.

A) 3.25
B) 1.26
C) -2.36
D) -4.65.

Question 10

One can convert all variables in a regression equation for comparative purposes by calculating the ______.

A) beta weight
B) partial slope coefficient
C) partial regression coefficient
D) R2

Question 11

Calculation of the standardized partial slopes is obtained by ______.

A) dividing the standard deviation of the dependent variable by the standard deviation of the independent variable
B) dividing the standard deviation of the independent variable by the standard deviation of the dependent variable
C) dividing the variance of the dependent variable by the variance of the independent variable
D) dividing the variance of the independent variable by the variance of the dependent variable

Question 12

With a regression equation with two independent variables, an R2 of .42 indicates that ______.

A) both of the independent variables explain 18% of the variation in the dependent variable
B) both of the independent variables cause 42% of the dependent variable
C) both of the independent variables explain 42% of the variation in the dependent variable
D) both of the independent variables cause 18% of the dependent variable

Question 13

For Model 1, the R² equals .23 and for Model 2 the R² = .35. This means that ______.

A) Model 2 explains an extra 12% of the variation in the dependent variable
B) Model 1 explains an extra 12% of the variation in the dependent variable
C) Model 1 was spurious and thus not explaining enough of the variation in the dependent variable
D) Model 1 was multicollinear and thus not explaining enough of the variation in the dependent variable

Question 14

The null hypothesis of a regression equation with three independent variables can be stated as ______.

A) $\beta_{1}, \beta_{2}, \beta_{3} \neq 0$
B) $\beta_{1}, \beta_{2}, \beta_{3}=0$
C) $\beta_{1}, \beta_{2}, \beta_{3}>0$
D) $\beta_{1}, \beta_{2}, \beta_{3}<0$

Question 15

To obtain the t-statistic of a regression equation, one must ______.

A) divide the standard error of the slope by the partial slope coefficient
B) divide the partial slope coefficient by the standard error of the slope
C) divide the mean square for the regression model by the mean square for the residuals
D) divide the mean square for the residual by the mean square for the regression model

Question 16

To obtain the F-statistic of a regression equation, one must ______.

A) divide the standard error of the slope by the partial slope coefficient
B) divide the partial slope coefficient by the standard error of the slope
C) divide the mean square for the regression model by the mean square for the residuals
D) divide the mean square for the residual by the mean square for the regression model

Question 17

As compared to the R2, the adjusted R2 ______.

A) takes into account the number of observations
B) takes into account multicollinearity
C) takes into account spuriousness
D) takes into account the number of independent variables in the regression equation

Question 18

Since researchers cannot always conduct true experiments, one must control for spurious relationships.

Question 19

To use the multiple regression equation the dependent variables and all of the independent variables have to be measured at the interval or ratio level.

Question 20

In order to compare the effects of two or more independent variables on a dependent variable the beta weight would be the proper statistic to use.

Question 21

The magnitude of R² does not change depending on which independent variable the researcher enters into the equation first.

Question 22

You can determine which independent variable has the strongest effect on the dependent variable by comparing unstandardized partial slope coefficients.

Question 23

The following diagram suggests that the relationship between X and Y is spurious due to Z

Question 24

The following diagram suggests that the relationship between X and Y is properly temporally ordered where the independent variables comes before the dependent variable.

Question 25

The following diagram suggests that the relationship between X1 and Y would be spurious due to X2. Thus, to get accurate estimates of the effect of X1 on Y one must control for X2.

Question 26

Explain the issues that arise with multicollinearity.

Question 27

A researcher is analyzing whether the rate of unlawful breaking is effected by the percent of poverty, percent male, percent nonwhite, and the percent of individuals between the ages of 15 and 24 residing in the census block. Given the following SPSS output, what would the researcher conclude? State the null and alternative hypotheses, discuss the F-statistic, the R², R² change, the beta coefficients, and which variable significantly affect the dependent variable.
a. Predictors: (Constant), percent nonwhite, percent poverty
b. Predictors: (Constant), percent nonwhite, percent poverty, percent 15 to 24, percent male a. Dependent Variable: rateofubev
b. Predictors: (Constant), percent nonwhite, percent poverty
c. Predictors: (Constant), percent nonwhite, percent poverty, percent 15 to 24, percent male a. Dependent Variable: rateofubev