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# Multivariate Statistics

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Question 1
Regression model results can be erroneous if multicollinearity is an issue. What causes multicollinearity?
a) A test of homogeneity of variance-covariance matrices is significant.
b) The DV is highly intercorrelated with one or more of the IV's.
c) One or more of the IV's are highly intercorrelated.
d) Non-linear data.

Question 2
If the intercept is statistically significant, what does this tell you?
a) The overall model is statistically significant.
b) There is significant variability among participants.
c) The assumption of homogeneity of variance has been violated.
d) None of the above.

Question 3
You decide that certain variables are more influential than others (based on previous research); these variables will be entered into your model first. What is this general modeling approach called?
a) Heirarchical Multiple Regression
b) Stepwise Regression
c) Backwards Regression
d) Linear Models Regression

Question 4
What is a common criticism of the STEPWISE method of variable selection?
a) The variables selected for entry are based on theory.
b) The variables selected for entry are chosen by the researcher.
c) The variables selected for entry are based solely on statistical means.
d) BACKWARD is always the better choice.

Question 5
If the Komogrorov-Smimov test is statistically significant, what does this tell you?
a) The assumptions of normality are likely met.
b) The assumptions of normality are likely not met.
c) The assumption of homogeneity of variance is likely not met.

Question 6
If the tolerance statistic is less than .1, what can you conclude?
a) Multicollinearity is likely to exist.
b) Multicollinearity is likely to not exist.
c) The overall regression model is likely to be significant.
d) The overall regression model is likely to be not significant.

Question 7
In path analysis, what is the "disturbance term"?
a) This is equal to one minus the path coefficient.
b) This is the amount of variance in the outcomes explained by the predictor.
c) A measure of how large the model is.
d) Direct effects on the outcome that are not attributable to the predictor variables.

Question 8
Which of the following is/are advantages of path analysis over regression analysis?
a) Path Analysis allows the incorporation of direct and indirect effects.
b) Path analysis allows one to test the fit of the overall model to the data.
c) Both A and B.
d) None of the above.

Question 9
What should you do with cases whose Mahalanobis distance exceeds the chi-squared critical value for the number of variables?
a) Eliminate the cases.
b) Transform the data.
c) Use regression instead of Path Analysis.
d) None of the above.

Question 10
In the scatterplot, you determine that the relationships between two variables curves. What should you do?
a) Eliminate the variable from analysis.
c) Transform the variable.
d) None of the above.

Question 11
The amount of total variance that is explained by any given factor is called:
a) eigenvector
b) eigenvalue
c) rotation
d) orthonormality.

Question 12
Which of the following are criteria for determining the number of factors/components to retain?
a) The point on the scree plot where the elbow occurs.
b) Eigenvalues greater than 1.0.
c) Assessment of model fit.
d) All of the above.

Question 13
What is the value of the communality that you should use to judge whether or not the eigenvalue criteria is reasonable?
a) .5
b) .7
c) 1.0
d) None of the above.

Question 14
Which test would you use to describe the major differences among groups following a MANOVA?
a) ANCOVA
b) Path Analysis
c) Multicollinearity
d) Discriminant Function Analysis

Question 15
How should you compute the effect size of a Discriminant Function model?
a) Square the canonical correlation.
b) Use the value for R-squared.
c) Use the value for Adjusted R-squared.
d) Use Wilks' Lambda.

Question 16
You have two models that have the following values for -2 Log Likelihood: Model 1 (125.43) and Model 2 (473.6). Which of the two models represents the better fit to the data?
a) Model 1
b) Model 2.
c) Both models might fit equally well.
d) It is impossible to tell.

Question 17
The odds ratio for one of your predictors is .995. What can you probably say?
a) Since the maximum is 1.0. this represents an almost perfect correlation.
b) The tolerance is too high, and multicollinearity is probably an issue
c) This measure is probably not a significant predictor of the outcome.
d) It is not possible to tell without other model fit in format

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#### Solution Summary

This solution is comprised of answer to objective questions. This is a advance statistics and best known as Multivariate Statistics. There are 17 questions and answers are highlighted in yellow color.

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