Question 1

A partial correlation where X₃is partialed out from the correlation between X₁and X₂indicates which one of the following? A) Both X₁ and X₃have been adjusted for X₂ B) The linear relationship between X₂and X₃are independent of the linear influence of X₁ C) The influence of X₂is removed from both X₁ and X₃ D) X₃is the control variable

Accepted Answer

X₃ is held constant (i.e., controlled or partialed out). That is, the influence of X₃ is removed from both X₁ and X₂ (both have been adjusted for X₃). Thus the partial correlation here represents the linear relationship between X₁ and X₂independent of the linear influence of X₃.

Question 2

In the event of perfect collinearity, which one of the following can occur?
A) The partial correlation can be greater than its corresponding bivariate correlation
B) The partial correlation can be less than its corresponding bivariate correlation
C) The partial correlation can be equal to zero when its bivariate correlation is not
D) All of the above
E) None of the above
Feedback: Perfect collinearity is a serious problem that can cause any option, a, b, or c, to occur.

Accepted Answer

Perfect collinearity is a serious problem that can cause any option, a, b, or c, to occur.

Question 3

Semipartial correlations are also referred to as which one of the following?
A) multicollinearity
B) part correlation
C) partial correlation
D) singularity

Accepted Answer

Semipartial correlations are also called part correlations.

Question 4

Which one of the following reflects a semipartial correlation? A) bivariate correlation between X₁ and X₂ B) correlation between X₁ and X₂ where X₃ is removed from X₂ only C) correlation between X₁ and X₂ where X₃ is removed from X₁ and X₂ D) perfect correlation between X₁ and X₂

Accepted Answer

An example of a semipartial correlation is the correlation between X₁ and X₂ where X₃ is removed from X₂ only. That is, the influence of X₃ is removed from X₂ only.

Question 5

The coefficient of multiple determination provides what type of information? A) the correlation between X₁ and X₂ where X₃ is removed from X₂ only B) the linear relationship between X₂ and X₃ that are independent of the linear influence of X₁ C) the number of standard deviations difference between groups D) the proportion of total variation in the dependent variable Y that is predicted from the set of predictor variables

Accepted Answer

The coefficient of multiple determination provides information on the proportion of total variation in the dependent variable Y that is predicted from the set of predictor variables.

Question 6

Sample standardized partial slopes are sometimes also referred to as which one of the following?
A) beta weights
B) bivariate correlations
C) part correlations
D) partial correlations

Accepted Answer

Sample standardized partial slope are sometimes called beta weights.

Question 7

In a standardized prediction model, the dependent variable equals which one of the following when the values of the independent variables are equal to their means?
A) 0
B) > +1
C) < −1
D) unable to determine without knowledge of the model

Accepted Answer

In a standardized prediction model, the dependent variable will equal zero when the values of the independent variables are equal to their means-i.e., zero).

Question 8

In which of the following cases will the adjustment for R² squared be large? A) When the assumptions of the test are met B) When the coefficient of multiple determination is zero C) When n is large relative to the total number of independent variables D) When n is small relative to the total number of independent variables

Accepted Answer

When n is small relative to m, the amount of bias can be large as R² can be expected to be large by chance alone. In this case the adjustment will be quite large.

Question 9

The test of significance of the coefficient of multiple determination tests which one of the following?
A) each individual partial slope
B) each regression coefficient in the model
C) individual unstandardized regression coefficients
D) overall model fit of the independent variables in aggregate

Accepted Answer

The first test is the test of significance of the overall regression model, or alternatively the test of significance of the coefficient of multiple determination. This is a test of all of the b_k's simultaneously, an examination of overall model fit of the independent variables in aggregate.

Question 10

Which one of the following methods of entering predictors eliminates predictors based on their minimal contribution to the prediction of the dependent variable?
A) backward elimination
B) forward selection
C) simultaneous entry
D) stepwise selection

Accepted Answer

With backward elimination, variables are eliminated from the model based on their minimal contribution to the prediction of the criterion variable.

Quiz 4: Multiple Linear Regression

A partial correlation where X3 is partialed out from the correlation between X1and X2 indicates which one of the following?

In the event of perfect collinearity, which one of the following can occur?

Semipartial correlations are also referred to as which one of the following?

Which one of the following reflects a semipartial correlation?

The coefficient of multiple determination provides what type of information?

Sample standardized partial slopes are sometimes also referred to as which one of the following?

In a standardized prediction model, the dependent variable equals which one of the following when the values of the independent variables are equal to their means?

In which of the following cases will the adjustment for R2 squared be large?

The test of significance of the coefficient of multiple determination tests which one of the following?

Which one of the following methods of entering predictors eliminates predictors based on their minimal contribution to the prediction of the dependent variable?

A partial correlation where X₃is partialed out from the correlation between X₁and X₂indicates which one of the following?

In which of the following cases will the adjustment for R² squared be large?