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9…Assessing a Model’s Fit and Predictive Ability

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11 Binary Logistic Regression

Table 11.13 Variables in the equation

B

Step 1a

a

age

Gender(1)

Income

No_Dep(1)

Job(1)

Education(1)

Other_Loan(1)

Constant

0.035

-1.536

0.010

-0.244

-0.681

-0.861

1.749

-4.118

S.E.

Wald

df

Significant

Exp(B)

0.015

0.526

0.004

0.298

0.307

0.331

0.616

1.056

5.194

8.511

7.510

0.672

4.922

6.786

8.053

15.195

1

1

1

1

1

1

1

1

0.023

0.004

0.006

0.412

0.027

0.009

0.005

0.000

1.036

0.215

1.010

0.784

0.506

0.423

5.749

0.016

Variable(s) entered on step 1: age, Gender, Income, No_Dep, Job, Education, Other_Loan

log odds of a positive response (probability modelled for Non-Defaulter = 1) as a

linear combination the predictor variables. This is written as follows:

ProbNonÀdefaulter

1 À ProbNonÀdefaulter

¼ À4:118 þ 0:035 Ã Age À 1:536 Ã Gender þ 0:010 Ã Income

LOGITi ¼ ln

À 0:244 Ã Number of Dependents À 0:681 Ã Job

À 0:861 Ã Education þ 1:749 Ã OtherLoan

SPSS will give the output of both logistic coefficients and exponentiated

logistic coefficients. According to Hair et al. (2010), the original logistic coefficients are most appropriate for determining the direction of the relationship and

less useful in determining the magnitude of relationships. Exponentiated coefficients directly reflect the magnitude of the change in the odds value. Because they

are exponents, they are interpreted with slight difference. The exponentiated

coefficients less than 1.0 reflect negative relationships, while values above 1.0

denote positive relationships.

Age: This is the estimated logistic regression coefficient for the variable age,

given the other variables are held constant in the model. The difference in log-odds

is expected to be 0.035 units higher for non-defaulter compared with defaulter,

while holding the other variables constant in the model. We got an exponentiated

coefficient value of 1.036 for age. For assessing magnitude, the easier approach to

determine the change in probability from these values is:

Percentage change in odds = (Exponentiated coefficient-1.0) * 100

= (1.036-1) * 100 = 3.6 %

which means if the exponentiated coefficient is 1.036, a one unit change in the

independent variable will increase the odds by 3.6 %.

Gender (1): This is a dichotomous independent variable and we considered

male group (male = 1, female = 0) as our reference category. The value we

estimated is the estimate logistic regression coefficient for a one unit change in

gender, given the other variables in the model are held constant. The logit

11.9

Assessing a Model’s Fit and Predictive Ability

257

coefficient for gender is -1.536 for the reference category (males) in terms of

females. The coefficient value is negative, which means the reference category will

have a negative impact on non-defaulter or the male group decreases the likelihood

of being a non-defaulter compared with females. The percentage of change in odds

is 78.5 %, which means the exponentiated coefficient is 0.215; a one unit change in

the independent variable (males) will decrease the odds by 78.5 %.

Intercept: This is the logistic regression estimate when all variables in the

model are evaluated

Note: Interpretation of the remaining coefficients in the same manner.

Standard Error: These are the standard errors of the individual regression

coefficients. They are used in both the 95 % Wald Confidence Limits.

The Wald Chi square test statistic is the squared ratio of the Estimate to the

Standard Error of the respective predictor. The Wald value follows a central Chi

square distribution with degrees of freedom given by DF, which is used to test

against the alternative hypothesis that the Estimate is not equal to zero. The

probability that a particular Wald test statistic is as extreme as, or more so, than

what has been observed under the null hypothesis is defined by Pr > ChiSq.

DF: This column gives the degrees of freedom corresponding to the Parameter. Each Parameter estimated in the model requires one DF and defines the Chi

square distribution to test whether the individual regression coefficient is zero,

given the other variables are in the model.

Chi Square and Pr > ChiSq: These are the test statistics and p-values,

respectively, testing the null hypothesis that an individual predictor’s regression

coefficient is zero, given the other predictor variables are in the model.

11.10

Questions

1. Which of the following is true?

(a)

(b)

(c)

(d)

Binomial logistic regression is the same as multiple regression

Binomial logistic regression can only be used with scores.

Binomial logistic regression is not at all like multiple regression

Binomial logistic regression is analogous to multiple regression

2. The logit value in logistic regression is

(a)

(b)

(c)

(d)

Is the cube root of the sample size

Is an instruction to record the data

Is a logarithm of a digit

Is the natural logarithm of the odds ratio

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11 Binary Logistic Regression

3. In binary logistic regression, the dependent variable is

(a)

(b)

(c)

(d)

Metric and non-categorical

Non-metric and dichotomous

It can be metric or non-metric

None of these

4. Logistic regression follows a distribution of

(a)

(b)

(c)

(d)

Normal

Binomial

Poisson

Skewed-Normal

5. The shape of logistic curve is

(a)

(b)

(c)

(d)

S-Shaped

L-Shaped

U-Shaped

Inverted U-shaped

Part V

Data Presentation

Chapter 12

Business Research Reports

Market researchers and decision makers conduct research on various problems/

opportunities and base their future decisions on the findings of the research. Unless

the research results are properly communicated in the reports, they would be of

little use to managers. Managers cannot take valid and effective decisions unless

the entire research findings are presented to them in a systematic manner.

A business research report contains many items including findings, analysis,

interpretations, conclusions and at times recommendations. These can be presented

to the management either in a written form or communicated orally. For the

research findings to be useful to the managers, the research report needs to be

meticulously designed, with all the necessary contents properly arranged and

presented.

This chapter deals with the fundamentals of report writing and presentation.

The chapter begins with a description of the types of research reports, provides

an insight into the various components of the written business research report

and concludes with a description of the features of written and oral

presentation.

12.1 Types of Research Reports

12.1.1 Short Reports

Short research reports usually run into 4–5 pages and are prepared for those

researches, which have a well-defined problem, limited scope and employ a clearcut methodology. These reports usually start with a concise statement regarding

the approval for the study, followed by the objective of the study, that is, the

problem definition and the research overview, which contains concisely, the main

part of the research, such as the methodology used. This is followed by conclusions based on the findings and recommendations, if any. The underlying basis for

S. Sreejesh et al., Business Research Methods,

DOI: 10.1007/978-3-319-00539-3_12,

Ó Springer International Publishing Switzerland 2014

261

262

12

Business Research Reports

these types of reports is to make information available, to all those concerned, in

an easy-to-use format. Short reports are prepared even for small clients who have

inexpensive projects.

12.1.2 Long Reports

As the name indicates, long reports are more detailed than the short reports. They

can be further subdivided into technical and management reports based on the

objectives of the researchers’ and the end users’. Technical reports (TRs) are

primarily meant for researchers. Management reports are meant for managers (as

end users), to aid their decision-making.

12.1.2.1 The Technical Report

A TR should focus on a specific topic logically pertaining to the research objective. The report should include the following: a descriptive title, author name and

information, date, list of keywords, informative abstract, body, acknowledgments,

list of references and appendices. The introduction of each TR should clearly

identify its thesis and an organizational plan for the same.

The body should consist of sources of data, research procedures, sampling

design, and data collection methods, instruments used, and data analysis arranged

into a standard format under motivation, methods, results and discussion. The TR

should include sufficient procedural information for other users to replicate the

study. Therefore, it should explain what was done, why it was done, what was

discovered and what was significant in the findings. The report should identify

clearly what is original about the work, and how it relates to past knowledge.

There is no minimum or maximum length requirement for a TR. However,

usually they are of 10–15 pages. A good quality TR should have the conclusions

and recommendations in line with the findings. While all necessary details should

be referred to, it should avoid the inclusion of non-essential information and

oversimplification.

12.1.2.2 The Management Report

Managers and decision-makers want information quick and straight to the point.

Therefore, they show little interest in knowing the technicalities of the research.

They are more interested in the ultimate findings and conclusions, which can act as

a base for their decisions. As the management reports are meant for a non-technical audience, there should be very less use of technical jargons and wherever

jargons are used, they should be explained using a footnote or in the appendices.

The language of a management report should be such that it is easy to understand.

Some of the other features of a good management report are as follows:

## 2014 s sreejesh, sanjay mohapatra, m r anusree (auth ) business research methods an applied orientation springer international publishing (2014)

## Part IV: Multivariate Data Analysis Using IBM SPSS 20.0

## 3…Role of Business Research in Decision-Making

## 6…Business Research and the Internet

## 1…Steps in the Research ProcessSteps in the Research Process

## 2…Part I: Exploratory Research Design

## 3…Part II: Descriptive Research Design

## 6…Errors in Survey Research

## 8…Part III: Causal Research Design

## 11…Type of Experimental DesignsExperimental designs

## 1…Identifying and Deciding on the Variables to be Measured

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