# Quiz 18: Discriminant and Logit

Business

Q 1Q 1

In multiple discriminant analysis, the interpretation of results is aided by an examination of all of the following except .
A) the structure correlations
B) the correlation coefficients
C) the standardized discriminant function coefficients
D) certain plots

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B

Q 2Q 2

As one of the statistics associated with discriminant analysis, the _ for each predictor is the ratio of the within- group sum of squares to the total sum of squares. Its value varies between 0 and 1.
A) Wilks' h
B) discriminant scores
C) discriminant function coefficients
D) eigenvalue

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Multiple Choice

A

Q 3Q 3

When the dependent variable is binary and there are several independent variables that are metric, in addition to two- group discriminant analysis all of the following models can be used except .
A) the probit model
B) the logit model
C) OLS regression
D) multiple discriminant analysis

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D

Q 4Q 4

If you are using the direct method or stepwise discriminant analysis, you are at the step of conducting discriminant analysis.
A) formulate the problem
B) determine the size of the discriminant function
C) assess the validity of the discriminant analysis
D) estimate the discriminant function coefficients

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Q 5Q 5

As one of the statistics associated with discriminant analysis, are obtained when the unstandardized coefficients are multiplied by the values of the variables and the products are summed and added to the constant term.
A) Wilks' h
B) discriminant scores
C) discriminant function coefficients
D) eigenvalue

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Q 6Q 6

Which of the following statements is true about stepwise discriminant analysis?
A) The predictor with the highest F ratio is the first to be selected for inclusion in the discriminant function, if it meets certain significance and tolerance criteria.
B) The predictors are entered sequentially based on their ability to discriminate between groups.
C) Each predictor selected is tested for retention based on its association with the other predictors selected.
D) All of the above statements are true.

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Q 7Q 7

In discriminant analysis, the criterion or dependent variable is and the predictor or independent variables are in nature.
A) ordinal; categorical
B) ordinal; interval
C) categorical; interval
D) interval; categorical

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Q 8Q 8

Sometimes also called confusion or prediction matrix, the contains the number of correctly classified and misclassified cases.
A) classification matrix
B) pooled within- group correlation matrix
C) identity matrix
D) total correlation matrix

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Q 9Q 9

Which of the following is not one of the steps involved in the "formulating the problem" step in discriminant analysis?
A) Estimate the discriminant function coefficients.
B) Repeatedly conduct the validation of the discriminant function.
C) Divide the sample into analysis and validation samples.
D) Convert the dependent variable into categories.

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Q 10Q 10

If you are using the leave- out option of SPSS, you are at the _ step of discriminant analysis.
A) determine the significance of the discriminant function
B) interpret the results
C) assess validity of discriminant analysis
D) estimate the discriminant coefficients

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Q 11Q 11

The is used for estimating the _ ; the _ _ is used for developing the .
A) validation sample; discriminant function; analysis sample; classification matrix
B) classification matrix; discriminant function; validation sample; analysis sample
C) analysis sample; discriminant function; validation sample; classification matrix
D) none of the above

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Q 12Q 12

As one of the statistics associated with discriminant analysis, the _ (unstandardized) are the multipliers of variables when the variables are in the original units of measurement.
A) Wilks' h
B) discriminant scores
C) discriminant function coefficients
D) eigenvalue

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Multiple Choice

Q 13Q 13

Which of the following statements is not an objective of discriminant analysis?
A) determination of which predictor variables contribute to most of the intergroup differences
B) evaluation of the accuracy of classification
C) classification of cases to one of the groups based on the values of the predictor variables
D) examination of whether significant differences exist among the groups, in terms of the criterion variables

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Q 14Q 14

The is a test of significance of the logistic regression coefficient based on the asymptotic normality property of maximum likelihood estimates.
A) Nagelkerke R2
B) Cox and Snell R square
C) Wilks' h
D) Wald statistic

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Q 15Q 15

A _ is a tool for assessing discriminant analysis results that plots the group membership of each case on a graph.
A) pie chart
B) territorial map
C) scattergram
D) characteristic profile

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Q 16Q 16

Discriminant analysis can be used to answer questions such as .
A) How much of the variation in sales can be explained by advertising expenditures, prices, and level of distribution?
B) In terms of demographic characteristics, how do customers who exhibit store loyalty differ from those who do not?
C) What are the distinguishing characteristics of consumers who respond to direct mail solicitations?
D) Both B and C are correct.

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Multiple Choice

Q 17Q 17

When the probability of success, P is modeled using a binary logit model, it is constrained to lie between _ .
A) - 1 and 1
B) 0 and - 1
C) 0 and 1
D) 1 and 100

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Q 18Q 18

Discriminant/logit analysis is similar to regression and ANOVA in which of the areas stated below (Table 18.1 in the text)?
A) nature of the dependent variables
B) nature of the independent variables
C) both A and B
D) none of the above

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Q 19Q 19

If there are 10 groups and 8 predictors, how many discriminant functions can be estimated?
A) ten
B) nine
C) eight
D) seven

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Q 20Q 20

The assumptions in discriminant analysis are that each of the groups is a sample from a _ population and all of the populations have the same .
A) multivariate normal; variance
B) multivariate normal; covariance matrix
C) multivariate normal; standard deviation
D) multivariate normal; standard error

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Q 21Q 21

Discriminant/logit analysis is similar to regression and ANOVA in which of the areas stated below (Table 18.1 in the text)?
A) number of dependent variables
B) number of independent variables
C) both A and B
D) none of the above

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Q 22Q 22

The binary logit model is also called .
A) logistic regression
B) OLS regression
C) stepwise regression
D) none of the above

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Q 23Q 23

An examination of differences across groups lies at the heart of the basic concept of .
A) regression analysis
B) conjoint analysis
C) discriminant analysis
D) factor analysis

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Q 24Q 24

What does it mean if the discriminant function is estimated and the square of the canonical correlation is .64?
A) The null hypothesis is not rejected. Therefore, there is no significant discrimination between groups.
B) 64% of the variance in the dependent variable is explained by the model.
C) 64% of the explained variance is accounted for.
D) B and C are correct.

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Q 25Q 25

In discriminant analysis, we can obtain some idea of the relative importance of the variables by .
A) examining the structure correlations, or canonical loadings or discriminant loadings
B) examining the absolute magnitude of the standardized discriminant function coefficients
C) examining the unstandardized discriminant function coefficients
D) A and B are correct

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Q 26Q 26

The linear combinations of independent variables developed by discriminant analysis that will best discriminate between the categories of the dependent variable are .
A) discriminant scores
B) discriminant functions
C) classification matrix
D) characteristic profiles

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Q 27Q 27

D is the in the model D = b

_{0 }+ b_{1}X_{1 }+ b_{2}X_{2 }+ b_{3}X_{3 }+ ... + b_{k}X_{k}. A) discriminant coefficient or weight B) difference variable C) disordinal interaction D) discriminant scoreFree

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Q 28Q 28

The nature of dependent and independent variables in the binary logit model is similar to that in .
A) regression analysis
B) multivariate analysis of variance
C) analysis of variance
D) discriminant analysis

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Q 29Q 29

Cox and Snell R square and Nagelkerke R2 are measures of model fit used in _.
A) logistic regression
B) OLS regression
C) the binary logit model
D) Both A and C are correct.

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Multiple Choice

Q 30Q 30

In discriminant analysis, there is no multicollinearity in the predictor variables. Therefore, there is no ambiguous measure of the relative importance of the predictors in discriminating between groups.

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True False

Q 31Q 31

With the leave- one- out cross- validation option in SPSS, the discriminant model is re- estimated as many times as there are respondents in the sample.

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True False

Q 32Q 32

In discriminant analysis, the value of the coefficient for a particular predictor depends on the other predictors included in the discriminant function.

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True False

Q 33Q 33

The logit model falls somewhere between regression and discriminant analysis in application.

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True False

Q 34Q 34

When the dependent variable is binary, the logit model can also be used instead of two- group discriminant analysis.

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True False

Q 35Q 35

In two- group discriminant analysis, it is possible to derive only one discriminant function.

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True False

Q 36Q 36

The binary logit model commonly deals with the issue of how likely an observation is to belong to each group. It estimates the probability of an observation belonging to a particular group.

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True False

Q 37Q 37

The direct method is an approach to discriminant analysis that involves estimating the discriminant function so that all the predictors are included simultaneously.

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True False

Q 38Q 38

When the probability of success, P, is modeled using OLS regression, P is constrained to lie between 0 and 1.

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True False

Q 39Q 39

When the criterion variable has two categories, the technique is referred to as multiple discriminant analysis.

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True False

Q 40Q 40

In discriminant analysis, rejecting the null hypothesis means there is significant discrimination between groups.

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True False

Q 41Q 41

In the discriminant analysis model, the coefficients, or weights (b), are estimated so that the groups differ as much as possible on the values of the discriminant function. This occurs when the ratio of between- group sum of squares to within- group sum of squares for the discriminant scores is at a maximum.

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True False

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True False

Q 43Q 43

The hit ratio is the number of variables found to be significant by the discriminant analysis.

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True False

Q 44Q 44

When the dependent variable is binary and there is one independent variable that is nonmetric, in addition to two- group discriminant analysis, one can also use OLS regression, logit, and probit models for estimation.

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True False

Q 45Q 45

The last step in conducting discriminant analysis is to interpret the results (Figure 18.2 in the text).

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True False

Q 46Q 46

The Mahalanobis procedure is based on minimalizing a generalized measure of the distance between the two closest groups.

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True False

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True False

Q 48Q 48

The first step in discriminant analysis is to formulate the problem by identifying the objectives, the criterion variable, and the independent variables.

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True False

Q 49Q 49

A characteristic profile is an aid to interpreting discriminant analysis results by describing each group in terms of the group means for the predictor variables..

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True False

Q 50Q 50

The results obtained from a classification matrix based on the analysis sample are invariably better than leave- one- out classification or the classification obtained on the holdout sample.

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True False

Q 51Q 51

The stepwise discriminant analysis method is appropriate when, based on previous research or a theoretical model, the researcher wants the discrimination to be based on all the predictors.

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True False

Q 52Q 52

When conducting discriminant analysis, the analysis sample is that part of the total sample used to check the results of the estimation sample.

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True False

Q 53Q 53

Discriminant functions are linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups).

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True False

Q 54Q 54

If attitude towards the brand is measured on a seven- point scale from unfavorable to favorable, it could be categorized as unfavorable (1, 2, 3), neutral (4), or favorable (5, 6, 7).

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True False

Q 55Q 55

The null hypothesis in discriminant analysis, that in the population, the means of all discriminant functions in all groups are not equal, can be statistically tested.

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True False

Q 56Q 56

The procedure that is used to estimate the parameters of the binary logit model is called the
maximum likelihood method.

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True False

Q 57Q 57

Also referred to as discriminant loadings, the structure correlations represent the simple correlations between the predictors and the discriminant function in discriminant analysis.

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True False

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Q 59Q 59

Discuss the similarities and differences among ANOVA, regression, and discriminant analysis (Table 18.1 in the text).

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