Deck 14: Multivariate Analysis

Question 1

Each of the following is key assumptions about the error term in a regression model, except:

A) Error variance is not constant (heteroscedasticity)
B) The expected value of the errors is 0: E( $\varepsilon$ _i) = 0
C) Errors are mutually independent: The correlation of $\varepsilon$ _i with $\varepsilon$ _j is zero
D) Errors are uncorrelated with any X

Answer 1

Error variance is not constant (heteroscedasticity)

Question 2

Each of the following is an important assumption about the errors terms in regression except:

A) Errors are uncorrelated with any X
B) Errors are systematic
C) Errors are mutually independent
D) The expected value of the errors is 0

Answer 2

B

Question 3

R squared is measured on scale from ___ to ____.

Answer 3

0, 1

Question 4

Please explain how you can control the effects of a third variable in a multivariate cross-tabulation by grouping.

Question 5

___________ means that there is constant variance, or that the variation in Y is the same at each level of X.

A) Multicolinearity
B) Spurious
C) Homoscedasticity
D) Interaction

Question 6

In a ____________ model, the expected value of the binary dependent variable or (what is the same thing) the probability that Y equals 1 is a linear function of the independent variables.

Question 7

A multivariate regression analysis requires a dependent variable with which level of measurement?

A) Nominal or ordinal
B) Nominal or ratio
C) Ordinal or interval
D) Interval or ratio

Question 8

_______ regression is a nonlinear model in which the log odds of one response as opposed to another is the dependent variable.

Question 9

To measure goodness of fit with a logistic regression, we commonly use ________ R squared instead of R squared.

Question 10

A ___________ variable is a hypothetical index that has just two values: 0 for the presence (or absence) of a factor and 1 for its absence (or presence).

A) Control
B) Third
C) Quantitative
D) Dummy

Question 11

__________ means the strength, direction, and nature of the X-Y relationship depends on levels of the control variable.

A) Interaction
B) Multivariate
C) Control by grouping
D) Multicolinearity

Question 12

In a multivariate cross-tabulation, we control for a third variable by ________.

A) Selection
B) Variance
C) Grouping
D) Means

Question 13

When analyzing data with a regression, statisticians are often concerned with the residuals. What are residuals and why are they important?

Question 14

A _____________ relationship is one in which the association between two variables is caused by a third.

A) Causal
B) Spurious
C) Spatial
D) Logistic

Question 15

Each of the following is an important assumption about the errors terms in regression except:

A) Errors are uncorrelated with any X
B) Errors are systematic
C) Errors are mutually independent
D) The expected value of the errors is 0

Question 16

A regression coefficient calculated from standardized variables is called a _________ regression coefficient, or, sometimes, a beta weight, and under certain, restricted circumstances might indicate the relative importance of each independent variable in explaining the variation in the dependent variable when controlling for all the other variables.

A) Standardized
B) Regularized
C) Interacted
D) Transformed

Question 17

What is meant by "controlling" for a third variable in a multivariate analysis?

Question 18

How would you test for statistical significance when performing a regression analysis using a t-test?

Question 19

The results from a standardized regression and the results from an unstandardized regression are similar in each of the following ways, except:

A) r will be interpreted the same way
B) R² will be interpreted the same way
C) The constant is interpreted the same way
D) t-Tests are interpreted the same way

Question 20

A logistic regression requires a ____________ dependent variable.

A) Ratio level
B) Dichotomous
C) Continuous
D) Constant

Question 21

Why is each β term in a multiple regression equation called a partial regression coefficient?

Question 22

What is the advantage of using a multiple regression to measure the relationships between three independent variables and a dependent variable instead of using three bivariate regressions to measure the relationships between each of the three independent variables and the dependent variable?

Question 23

What is multicolinearity and why is it important?

Question 24

How does standardizing a variable affect the interpretation of the variable in a regression?

Question 25

Please interpret the following multiple regression output table by indicating how you would interpret all of the statistics and coefficients we discussed in class. Make sure you interpret the relationship between each independent variable and the dependent variable and assess statistical significance.

Question 26

How can we use a nominal level variable like region (East, West, South, and Midwest) in a regression analysis? How would you manipulate the variable for inclusion in the regression equation?