978-1111826925 Chapter 24 Solution Manual

QUESTIONS FOR REVIEW AND CRITICAL THINKING/ANSWERS

1. Define multivariate statistical analysis.

Research that involves three or more variables, or that is concerned with underlying dimensions

2. What is the variate in multivariate? What is an example of a variate in multiple regression

and in factor analysis?

The variate is a mathematical way in which a set of variables can be represented with one

equation. Variates are formed as a linear combination of variables, each contributing to the

3. What is the distinction between dependence techniques and interdependence techniques?

If the technique attempts to explain or predict the dependent variable on the basis of two or more

independent variables, the researcher is investigating dependence. Multiple regression, multiple

4. What is the GLM? How can multiple regression and n-way ANOVA be described as GLM

approaches?

Multivariate dependence techniques are variants of the general linear model (GLM). Simply, the

GLM is a way of modeling some process based on how different variables cause fluctuations

5. What are the steps in interpreting a multiple regression analysis result? Can the same steps

be used to interpret a univariate ANOVA model?

Steps in interpreting a multiple regression model:

1. Examine the model F-test – if not significant, the model should be dismissed and there

is no need to proceed to further steps.

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4. Examine collinearity diagnostics – multicollinearity in regression analysis refers to

how strongly interrelated the independent variables in a model are.

For ANOVA, the steps involved are essentially the same with the addition of interpreting

differences between means.

6. A researcher dismisses a regression result because the model R2 was under 0.70. Do you

think this was necessarily wise? Explain.

No cut-off values exist when examining R2. However, the absolute value is more important when

7. Return to the simple example of regression results for the toy company presented in the

chapter. Since the data come equally from Europe and Canada, does this represent a

potential source of variation that is not accounted for in the researcher’s model? How could

the researcher examine whether or not sales may be dependent upon country?

Less than interval (non-metric) independent variables can be used in multiple regression. This

8. What is a factor loading?

9. How does factor analysis allow for data reduction?

Factor analysis is a technique of statistically identifying a reduced number of factors from a larger

number of measured variables. The factors themselves are not measured, but instead, they are

10. How is the number of factors decided in most EFA programs?

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11. What is multi-dimensional scaling? When might a researcher use this technique?

Multidimensional scaling provides a means for measuring objects in multidimensional space on

the basis of respondents’ judgments of the similarity of objects. The perceptual difference among

12. What is cluster analysis? When might a researcher use this technique?

Cluster analysis is a multivariate approach for identifying objects or individuals that are similar to

one another in some respect. It classifies individuals or objects into a small number of mutually

exclusive and exhaustive groups. Objects or individuals are assigned to groups so that there is

13. Name at least two multivariate techniques that can be useful in constructing perceptual maps.

There are multiple ways of using multivariate procedures to generate a perceptual map. For

14. A researcher uses multiple regression to predict a client’s sales volume based on gross

domestic product, personal income, disposable personal income, unemployment, and the

consumer price index. What problems might be anticipated with this multiple regression

model?

The predictor variables are all highly intercorrelated. Multicollinearity in regression analysis

refers to how strongly interrelated the independent variables in a model are. When

RESEARCH ACTIVITIES

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1. Use the multistep process to interpret the regression results below (see the textbook for the

results). This model has been run by a researcher trying to explain customer loyalty to a

restaurant. The independent variables are customer perceptions of value, atmosphere, quality

and a location variable labeled center. This is a dummy variable that takes the value of 1 if

the restaurant is in a shopping center an 0 if it is a stand-alone location. What substantive

conclusions would you recommend to the restaurant company?

Steps in interpreting a multiple regression model:

1. Examine the model F-test – if not significant, the model should be dismissed and there

is no need to proceed to further steps.

The model F of 7.049 is significant at the p < 0.05 level. The independent variables with

significant t-tests at the p < 0.05 level are Value and Center, and Atmosphere is significant at the p

2. Interpret the following GLM results (see the textbook for the results). Following from an

example in the chapter, performance is the performance rating for a business unit manager.

Sales is a measure of the average sales for that unit. Experience is the number of years the

manager has been in the industry. The variable dummy has been added. This variable is 0 if

the manager has no advanced college degree and a 1 if the manager has an MBA. Do you

have any recommendations?

Students should use the steps outlined in the previous activity to interpret the results. The overall

3. Interpret the following regression results (see the textbook for the results). All of the

variables are the same as in number 2. These results are produced with a regression program

instead of the GLM-univariate ANOVA program.

a. What do you notice when the results are compared to those in number 2? Comment.

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The model F-value and the p-value associated with it are identical. The t-values for the

b. List the independent variables in order from greatest to least in terms of how strong the

relationship is with performance.

When researchers want to know which independent variable is most predictive of the dependent

c. When might one prefer to use an ANOVA program instead of a multiple regression

program?

When the independent variables are less than interval.

4. Interpret the following factor analysis results (see the textbook for the results). The variables

represent sample results of self-reported emotions while viewing a film. Why are only two

factors reported below? What would you name the two summated scales which could be

produced based on these results.

Only two components have eigenvalues greater than 1.0. The rotated component matrix indicates

5. [Internet Question] Go to www.census.gov and examine some of the tables for your area. Cut

and paste the table into a spreadsheet or statistical program. Run one dependence and one

interdependence technique on the data. Interpret the results.

Students’ answers will vary. Possible dependence techniques covered in this chapter include

6. [Internet Question] Use http://www.ask.com to find an F-ratio calculator that will return a

p-value given a calculated F-ratio and the degrees of freedom associated with the test.

7. [Internet Question] The Federal Reserve Bank of St. Louis maintains a database called FRED

(Federal Reserve Economic Data). Navigate to the FRED database at

http://www.stls.frb.org/fred/index.html. Use the consumer price index, exchange rates,

interest rates and one other variable to predict the consumer price index for the same time

period. The data can either be downloaded or cut and pasted into another file.

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CASE 24.1 THE UTAH JAZZ

Objective: The case presents the statistical results of analysis of variance and multiple

discriminant analysis. The student is asked to interpret the findings.

Summary: The management of the Utah Jazz read an article dealing with market segmentation

in the professional basketball market. Data came from a survey of adult residents of a large

western metropolitan area. Respondents were selected in accordance with a quota sample of the

area that was based on the age and sex characteristics reported in the most recent census. Six age

categories for both males and females were used to gain representation of these characteristics of

the market. In addition, interviewers were assigned to various parts of the area to ensure

representation of the market with respect to socioeconomic characteristics, as well. A total of 225

respondents aged 18 and over provided data for the study.

Interviews were conducted by trained interviewers using a self-completion questionnaire. The

presence of the interviewers allowed for answering any questions that might arise, as well as

ensuring compliance with the instructions.

Measures for the variables in the three categories of AIO’s were obtained using six-point rating

scales. For example, the item for price proneness asked: When you are buying a product, such as

food, clothing, and personal care items, how important is it to get the lowest price? This item was

anchored with “Not at all important” and “Extremely important.” Several statistical tables are

presented in the case.

Question

Interpret the managerial significance of the ANOVA and multiple discriminant analysis results.

Quite clearly, the market segments for professional basketball can be characterized in terms of a

number of the variables taken from the previous studies that were considered to be relevant for

The following paragraphs summarize the nature of the three market segments that were examined

in the research, and offer implications of the empirical findings for management. Given the

High Attenders

Except for three items in the set of Opinions about Professional Sports, the relationships were

monotonic with increasing patronage. Thus, for the most part, the high attenders contrast to the

greater extent with the non-attenders, with the low attenders falling between these segments.

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The high attenders emerge as enthusiastic sports fans. They are sports fans in general, and the

NBA team provides but one means of satisfying their needs as spectators. Beginning in their early

years, they have both participated in sporting events and viewed them as spectators. They prefer

active forms of recreation and perceive themselves as athletic. Perhaps because of their own

athletic experiences, they choose to support a winner. Because of their age and dwelling, these

high attenders are more likely than members of other segments to be characterized as less

established in the community.

With respect to strategy, franchise management can first try to sell the attractiveness of sports in

general. Helping to increase attendance for a variety of local sporting events appears to be a way

to increase attendance at NBA games. Thus, to some extent, it may be profitable to sell sports

first, basketball second, and NBA basketball third. Management should sell their attraction on the

basis that this is an athletic event, not a theatrical performance. Perhaps they can most directly

reach members of this most salient market segment through other athletic facilities, such as

gymnasiums, spas, and through programs and signs at other sporting events.

Further, management should support athletic events around the community wherever possible. In

particular, developing an interest in sports in youngsters will have long-term profit implications

for the franchise. These marketers should help patrons (and non-patrons) to see themselves as

athletic, and should seek additional ways to help them identify with the professional athletes on

the basketball court.

This attempt to further develop their customers’ identification with athletics (and this form of

athletics in particular), may be successful to the extent it relates to one’s earlier experiences.

Potential customers can be shown the virtues of bringing a younger person to the next NBA game

with them, thus giving the youth the same good times they enjoyed as youngsters (and perhaps

reliving pleasant parts of their own childhood). At the extreme, such appeals to altruism can

suggest that “winning” need not be shown only on the scoreboard (perhaps a necessity if the local

team is one of the league’s doormats).

Low Attenders

The findings suggest that the low attender group may consist largely of the curious and those who

have attended a game with someone else who had a greater interest in the proceedings. These

infrequent patrons have not caught the excitement of the game and the enthusiasm of the sports

fans described in the preceding section. They are more accepting of the beer concession.

As this group falls generally between the other two segments, the first approach would likely be

to use the same strategy outlined above for the sports fans. But, given their several differences

from the other two segments, some variation on this strategy may be necessary. If so, these

customers must be shown that professional basketball is a suitable alternative to their preferred

way to spend an evening. Perhaps they can be encouraged to find an interest in “natural” rivalries

among teams, rather than to see animosity in the physical combat on the court.

Non-Attenders

The non-attenders are older, more established persons who have the least interest in sports of the

three segments. The data give little positive help in making appeals to them. Thus, it appears that

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efforts directed at these persons would best succeed if made in terms other than those suggested

for the heavy half of the patrons. Perhaps they will respond to messages about the important

tradition of having the team in the community and appeals based on how the team represents their

community throughout the country. The non-attenders may be shown the benefits of buying

tickets for others with a greater interest in sports, perhaps for business associates, employees, and

customers.

The findings for this group provide the clearest basis for suggestions for future research.

Non-attenders can be asked the attributes they find enjoyable in preferred leisure pursuits, then

asked to use these attributes to contrast NBA basketball with the more appealing alternatives.

They can be asked their reactions to specific aspects of strategy, such as pricing and scheduling of

games. They may further be asked to react to proposed changes in this strategy.

In conclusion, the AIOs provide a useful portrayal of the market, especially by characterizing the

frequent attenders—who, after all, are the bread-and-butter of the franchise. As is often the case,

demographics also help to portray the market, although in this case they were less suggestive than

usual of strategy.

CASE 24.2 How Do We Keep Them?

Data: Use the data labeled profit for this case.

Objective: The purpose of this case is to allow students to perform interdependence and

dependence techniques.

Summary: The data go along with the research snapshot labeled “Too much of a good thing,”

which illustrates the difficulty in interpreting regression results with several highly correlated

independent variables. Management wants to understand turnover of managers, and several

emotions to describe the way they feel about their job are measured using semantic differential

scales. Another variable, the likelihood a manager will quit within twelve months, is also

assessed. An initial regression model with eight independent variables predicting turnover was

confusing and difficult to make sense of. Thus, the researcher turned to a data reduction

technique to enable a regression with fewer independent variables. These are the tasks the

students must perform.

Questions

1. Perform the appropriate multivariate technique to identify underlying dimensions that may

exist among the emotion ratings.

Factor Analysis – there are multiple ways to approach this problem. Since the case set up implies

that management is interested in eight variables, the student should select the eight that make

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scales as described earlier. The user should note that the semantic differential for excitement is

split loaded and should not be included on any scale (it lacks discriminant validity).

Total Variance Explained

Component Initial Eigenvalues

Extraction Sums of Squared

Loadings

Rotation Sums of Squared

Loadings

Total

% of

Variance

Cumulative

% Total

% of

Variance

Cumulative

% Total

% of

Variance

Cumulative

%

12.706 33.823 33.823 2.70

633.823 33.823 2.702 33.772 33.772

21.492 18.651 52.474 1.49

218.651 52.474 1.485 18.561 52.333

Extraction Method: Principal Component Analysis.

Rotated Component Matrix(a)

Component

Positive Emotion Result Arousal

sdsatisfied Satisfied .970

sdhappy Happy .917

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

a Rotation converged in 5 iterations.

2. Create scales for any underlying dimensions.

Notice that in the component matrix above, the factors have been interpreted and provided names.

The scales that result from these will be used in the regression model (scales can be created with

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Reliability – only the most advanced students will realize that a coefficient alpha should be

computed for the Positive Affect Score, and the result is given below. Technically, coefficient

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Reliability Statistics

Cronbach’s

Alpha N of Items

.918 3

3. Use these scales as independent variables in a regression model.

Variables Entered/Removed(b)

Model

Variables

Entered

Variables

Removed Method

1Arousal,

Positive

Emotion(a)

a All requested variables entered.

b Dependent Variable: turnover Turnover Rating

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of

the Estimate

a Predictors: (Constant), Arousal, Result, Positive Emotion

ANOVA(b)

Model

Sum of

Squares df

Mean

Square F Sig.

a Predictors: (Constant), Arousal, Result, Positive Emotion

b Dependent Variable: turnover Turnover Rating

Coefficients(a)

Model Unstandardized Coefficients

Standardized

Coefficients t Sig. Collinearity Statistics

B Std. Error Beta t-value p-value

Tolerance VIF

1 (Constant) 1.351 4.703 .287 .776

a Dependent Variable: turnover Turnover Rating

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4. Interpret the results.

In contrast to the research snapshot result, the regression result here is very clean. The overall

model is significant and explains 49% of the variance in turnover. There is one significant Beta

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