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
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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: