Deck 10: Multiple Regression

Question 1

In multiple regression, the betas are

A) coefficients of alienation
B) coefficients of determination
C) standardized regression coefficients
D) unstandardized regression coefficients

Answer 1

standardized regression coefficients

Question 2

If you want to see how well percent of classes attended and percent of assigned reading completed do together in accounting for differences in student exam grades, what is an appropriate statistical technique to use?

A) Bivariate Correlation
B) Compute
C) Explore
D) Linear Regression

Answer 2

Linear Regression

Question 3

If you want to see which individual factor (age at marriage, educational level, or income) has the strongest association with marital happiness and you are not interested in controlling for other factors, what is an appropriate statistic to use?

A) mean
B) Pearson's r
C) standardized regression coefficient
D) unstandardized regression coefficient

Answer 3

Pearson's r

Question 4

The regression equation is Y = 50 - 5X₁ + 10X₂ - 20X₃. A case has a value of 1 on X₁, 2 on X₂, and 3 on X₃. What's the predicted value?

A) −2
B) 5
C) 35
D) 48

Question 5

If multicollinearity is present, one solution is to

A) add at least one more independent variable to the equation
B) remove one of the very strongly correlated independent variables from the equation
C) switch to a nominal dependent variable
D) use the values of the unstandardized and standardized coefficients but not use the values for R and R²

Question 6

If you want to see which factor (age at marriage, educational level, or income) had the strongest net effect on marital happiness, what is an appropriate statistical technique to use?

A) Bivariate Correlation
B) Compute
C) Explore
D) Linear Regression

Question 7

The regression coefficients for two independent variables that are very strongly related to one another may not be very stable. This regression problem is referred to as

A) dummy variables
B) heteroscedasticity
C) multicollinearity
D) serial correlation

Question 8

If the variables in this matrix were all used as independent variables in a regression equation, would there be a multicollinearity problem?
 

A) no
B) yes due to the correlation between ACT and SAT
C) yes due to the correlation between BIRTH and HSRank
D) yes due to the correlation between HSRank and SAT

Question 9

In multiple regression, the slopes are

A) coefficients of alienation
B) coefficients of determination
C) standardized regression coefficients
D) unstandardized regression coefficients

Question 10

In order to use a nominal variable that has four attributes as an independent variable in multiple regression, you should

A) convert it into a series of dummy variables
B) create a multicollinearity trap
C) run a scatterplot to be sure it has a linear effect
D) transform it into a standardized variable

Question 11

Which of the following statements is correct?

A) An ordinal variable with three or more categories can be the dependent variable in regression.
B) An interval/ratio variable with three or more categories can be the dependent variable in regression.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 12

Which of the following statements is correct?

A) Standardized regression coefficients (betas) indicate the direction of a relationship.
B) A nominal variable with three or more categories can be the dependent variable in regression.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 13

Dummy variables are a way to include into a regression analysis

A) nominal variables as dependent variable
B) nominal variables as independent variables
C) ordinal variables as dependent variables
D) ordinal variables as independent variables

Question 14

The regression equation is POVERTY = 10 + 1(UNEMPLOYMENT) - 0.5(COLLEGE). A county has a POVERTY rate of 30, an UNEMPLOYMENT rate of 10, and COLLEGE graduate rate of 10. What is the county's regression residual?

A) −50
B) −15
C) 15
D) 50

Question 15

Multicollinearity is when there _____ among the independent variables in a regression equation. For the person wanting to do a regression analysis, multicollinearity is a _____ thing.

A) are no very strong correlations . . . bad
B) are no very strong correlations . . . good
C) is at least one very strong correlation . . . bad
D) is at least one very strong correlation . . . good

Question 16

A researcher regresses a quality-of-life INDEX on INCOME and EDUCATION. The Y-intercept is 10, the slope for INCOME is +2, and the slope for EDUCATION is −1. What's the correct regression equation?

A) INDEX = 11
B) INDEX = 10 + 2 - 1
C) INDEX = 2(INCOME) - 1(EDUCATION)
D) INDEX = 10 + 2(INCOME) - 1(EDUCATION)

Question 17

What types of dependent variables are ok to use for linear regression?

A) interval/ratio variables
B) interval/ratio variables and dichotomies
C) interval/ratio variables, ordinal variables, and dichotomies
D) interval/ratio variables, ordinal variables, and nominal variables

Question 18

If you want to see the net effect of gender on academic achievement after controlling for age and parents' social class, what is an appropriate statistical technique to use?

A) Bivariate Correlation
B) Compute
C) Frequencies
D) Linear Regression

Question 19

What proportion of the differences in the dependent variable is explained by the independent variables in the regression equation?
 

A) .151
B) .388
C) .612
D) .849

Question 20

Which independent variable has the strongest net effect on GPA?
 

A) SAT
B) HSRank
C) BIRTH

Question 21

What information does a standardized coefficient provide?

Question 22

How can a nominal variable with three attributes be used as a regression independent variable?

Question 23

What is a net effect?

Question 24

If you want to see what the cases in your data set are like on a single continuous, interval/ratio variable, what is an appropriate statistical technique to use?

A) Bivariate Correlation
B) Compute
C) Explore
D) Linear Regression

Question 25

For each of the following types of variables, indicate if it can be used in regression as a dependent variable and if it can be used as an independent variable by stating yes or no.

Question 26

Answer the questions that follow this SPSS output:

If the four variables in the correlation matrix were all used as independent variables in a single multiple regression analysis, would there be a multicollinearity problem?

A) State yes or no. __________
B) Justify your answer by referring to one or more statistics in the matrix.

Question 27

Describe the process of creating dummy variables so that the information contained in the nominal independent variable CAR (attributes: Ford, General Motors, Chrysler, other) can be included in a regression equation.

Question 28

When would you use unstandardized regression coefficients and when would you use standardized regression coefficients?

Question 29

Answer the questions that follow this SPSS output:

The dependent variable is fallGPA (student's GPA after the fall semester). The independent variables are sizeHS (the size of their high school graduating class) and SAT (their best SAT score).

A) What is the value of the multiple correlation (that is, the correlation between the dependent variable and the set of independent variables)?
B) What is the value of the coefficient of determination?
C) Of the two independent variables, which has the stronger net effect on the dependent variable?
D) Write out the regression equation. (You may use Y and X's in the regression equation or, in place of the Y and X's, you may use variable names.)

Question 30

Let's say the correlation between SAT scores and college GPA is .70 but when you regress college GPA on SAT scores and parents' social class, the standardized coefficient for SAT scores is .02. What would this tell you?

Question 31

For each of the following, indicate if it gives you information about the strength of a relationship and/or the direction of a relationship:

Question 32

What kinds of questions can you answer using multiple regression?

Question 33

An analyst is interested in the relationship between number of cats a person has (an independent variable), number of dogs a person has (an independent variable) and the number of friends the person has (the dependent variable). She regresses number of FRIENDS on number of CATS and number of DOGS. The equation for the best-fitting straight line is
FRIENDS = 10 − 2(CATS) + 1(DOGS)

A) A person had 4 cats and 2 dogs. What is that person's predicted number of friends?
B) What is the regression residual for a person with 0 cats, 0 dogs, and 0 friends?

Question 34

Answer the questions that follow this SPSS output:

The dependent variable is CHILDS (the number of children a person has). The independent variables are CATHOLIC (whether the person is Catholic or not), EDUC (the number of years of schooling completed by the person), and YRSMAR (the number of years the person has been married).

A) What is the value of the multiple correlation (that is, the correlation between the dependent variable and the set of independent variables)?
B) What proportion of the variability in number of children is explained by the three independent variables?
C) Of the three independent variables, which has the weakest net effect on the dependent variable?
D) Write out the regression equation. (You may use Y and Xs in the regression equation or, in place of the Y and Xs, you may use variable names. Don't forget the subscripts on the Xs if you use Y and Xs.)

Question 35

In the context of regression analysis, each of the following has at least one other name. State at least one of those other names:

Question 36

Answer the questions that follow this SPSS output:

If the three variables in the correlation matrix were all used as independent variables in a single multiple regression analysis, would there be a multicollinearity problem?

A) State yes or no. __________
B) Justify your answer by referring to one or more statistics in the matrix.

Question 37

When would you use Crosstabs to look at the net effects of two independent variables on a dependent variable and when would you use Linear Regression?

Question 38

What is multicollinearity and why is it a problem?

Question 39

According to the following regression equation: INCOME = 9000 + 2500(EDUC) − 100(AGE) − 5000(FEMALE), an increase of one year in education results in how much of a change in income? (State both the amount of change and the direction.)