Logistic regression measures the relationship between the categorical target variable and one or more independent variables It deals with situations in which the outcome for a target variable can have two or more possible types. The Multinomial-Logistic Regression Classification Algorithm is useful in identifying the relationships of various attributes, characteristics and other variables to a particular outcome.

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2. Multinomial Logistic
Regression

3. Terminologies
Introduction & Example
Standard input/tuning parameters & Sample UI
Sample output UI
Interpretation of Output
Limitations
Business use cases
What Are
All Covered

4. Terminologies

5. Terminologies
 Target variable usually denoted by Y , is the variable being predicted and is also
called dependent variable, output variable, response variable or outcome
variable (Ex : One highlighted in red box in table below)
 Predictor, sometimes called an independent variable, is a variable that is being
used to predict the target variable ( Ex : variables highlighted in green box in
table below )
Age Marital Status Gender
Satisfaction
level
58 married Female High
44 single Female Low
33 married Male Medium
47 married Female High
33 single Female Medium
35 married Male High
28 single Male Low

6. Introduction & Example

7. Introduction
• OBJECTIVE :
• Logistic regression measures the relationship
between the categorical target variable and one or
more independent variables
• It deals with situations in which the outcome for a
target variable can have two or more possible types
• Thus , logistic regression makes use of one or more
predictor variables that may be either continuous or
categorical to predict the target variable classes
• BENEFIT:
• Logistic regression model output helps identify
important factors ( Xi ) impacting the target variable
(Y) and also the nature of relationship between each
of these factors and dependent variable

8. Example : Multinomial Logistic Regression :
Input Let’s conduct the Multinomial Logistic Regression analysis on following variables :
Job satisfaction
level
Age Marital Status Gender Income
Low 58 married Male 46,399
Medium 44 single Male 47,971
Low 33 married Female 52,618
High 47 married Male 28,717
Medium 33 single Female 41,216
Medium 35 married Female 34,372
Low 28 single Male 64,811
Medium 42 divorced Female 53,000
High 58 married Female 41,375
Low 43 single Male 53,778
Low 41 divorced Male 44,440
Medium 29 single Female 51,026
Independent variables (Xi)Target Variable (Y)

9. Example : Multinomial Logistic Regression :
Output 1 Coefficient P value
High
Age 1.54 0.05
Income -0.34 0.03
Male 0.67 0.02
Low
Age -2.34 0.05
Income 0.56 0.01
Male -1.23 0.04
Coefficients
• High satisfaction with reference to medium satisfaction:
Age - Multinomial logit (Natural log of the proportion of High to that of Medium here)
estimate for 1 year increase in age for high job satisfaction relative to medium job satisfaction
when other independent variables are held constant = 1.54
Male - Multinomial logit estimate for comparing male to females for high job
satisfaction relative to medium job satisfaction when other variables are held constant = 0.67
Interpretation

10. Example : Multinomial Logistic Regression :
Output 2
Classification Accuracy : (50+ 10 + 70) / (50+ 10 + 70+ 4+4+5+4+6+7) = 81%
• The prediction accuracy is useful criterion for assessing the model performance
• Model with prediction accuracy >= 70% is useful
Classification Error = 100- Accuracy = 19%
There is 19% chance of error in classification
Low Medium High
Low 50 4 4
Medium 4 70 5
High 6 7 10
Actual versus predicted
Predicted
Actual

11. Standard input/tuning
parameters & Sample
UI

12. STANDARD
INPUT
PARAMETERS
& SAMPLE UI

13. SAMPLE OUTPUT UI

14. Sample output 1 : Model Summary
Actual versus predicted
Predicted
Actual
Coefficient matrix :
Low Medium High
Low 50 4 4
Medium 4 70 5
High 6 7 10
Coefficient P value
High
Age 1.54 0.05
Income -0.34 0.03
Male 0.67 0.02
Low
Age -2.34 0.05
Income 0.56 0.01
Male -1.23 0.04

15. Age Marital Status Gender Income
Job satisfaction
level
Predicted
class
Probability
58 married Female 46,399 Low Low 0.7
44 single Female 47,971 High High 0.9
33 married Male 52,618 Low Low 0.8
47 married Female 28,717 Low High 0.7
33 single Male 41,216 High Low 0.6
35 married Male 34,372 High High 0.5
28 single Female 64,811 Low Low 0.4
42 divorced Male 53,000 Low Low 0.3
58 married Female 41,375 High Low 0.2
43 single Male 53,778 High High 0.1
Sample output 2 : Predicted class &
probability

16. Sample Output 3 : Classification Plot
• Lesser the overlap among three classes in the plot above , better the classification done
by model
• Thus, output will contain predicted class column, confusion matrix and classification plot

17. Interpretation of
Output

18. Interpretation of Important Model Summary
Statistics
Accuracy:
 If Accuracy >= 70% : Model is well fit on
provided data and predicted classes are
reasonably accurate
 If Accuracy < 70% : Model is not well fit on
provided data and predicted classes are
likely to contain high chances of error
Coefficients and p value :
 If value of coefficient is positive and p value
<0.05 , variable is positively correlated with target
variable
 If value of coefficient is negative and p value
<0.05 , variable is negatively correlated with
target variable
 If p value > 0.05, variable is unimportant in terms
of predicting target variable classes

19. Limitations

20. Limitations
 It is applicable only when target variable is categorical
 Sample size must be at least 1000 in order to get reliable predictions
 Level 1 of the target variable should represent the desired outcome.
 i.e. if desired class is yes in response/non response target variable
then Yes has to be recoded into 1 and No into 0

21. Business Use Cases

22. Use case 1
Business benefit:
• By having a knowledge of probable
election outcome, proper strategy
can be put in place in case of
discrepancies between
expectations and predictions and
the segments with high likelihood
of voting oppositions can be
targeted in better and effective
manner in order to get their votes
in favor of a client party
Business problem :
• A research agency wants to predict
the likelihood of each election
candidate being voted by each
voter and in turn devise a strategy
to take proactive steps
• Here the target variable would be
‘preferred party name’ and
predictors would be customer
demographics such as age, income,
qualification, occupation, gender,
religion and past voting status etc.

23. Use case 1 : Sample Input Dataset
Responder
ID
Qualification income Age Gender Occupation
Done voting in
past
Preferred party
1039153 Bcom 105000 18 M Accountant yes ABC
1069697 12th
Pass 192000 20 F
Office
Supervisor
No XYZ
1068120 BSC 310000 30 F Pathologist yes PQL
563175 10th
Pass 100000 45 M Labour yes XYZ
562842 ME 357228 25 M
Software
Developer
No PQL
562681 MSC 413000 28 F Statistician yes XYZ
562404 BSC Nill 34 F Home maker No PQL

24. Use case 1 : Output : Predicted Class
Output : Each record will have a predicted class along with probability assigned as
shown below :
Respond
er ID
Qualificatio
n
Income Age Gender Occupation
Done
voting in
past
Predicted
party
Probability
1039153 Bcom 105000 18 M Accountant yes ABC 0.7
1069697 12th
Pass 192000 20 F
Office
Supervisor
No XYZ 0.9
1068120 BSC 310000 30 F Pathologist yes PQL 0.8
563175 10th
Pass 100000 45 M Labour yes XYZ 0.7
562842 ME 357228 25 M
Software
Developer
No PQL 0.6
562681 MSC 413000 28 F Statistician yes XYZ 0.5
562404 BSC Nill 34 F
Home
maker
No PQL 0.4

25. Use case 1 : Output : Sample Class profile
Predicted
Party
Average
Annual
income
Average
Age
ABC 86,467 30
XYZ 60,935 25
PQL 1,05,400 35
• As can be seen in the table above, there is distinctive characteristics of population associated with each preferred
party :
• For instance, females are inclined towards XYZ whereas males tend to prefer ABC
• Responders with high income and age prefer to vote for PQL whereas XYZ party is preferred by lowest income and
age group
• Fresh voters are likely to vote for party XYZ whereas those who have done voting in past are inclined towards ABC
party
Gender
Predicted
Party
Male Female
ABC 60 4
XYZ 10 78
PQL 14 15
Past voting status
Predicted
Party
Yes No
ABC 58 6
XYZ 15 73
PQL 11 19

26. Use case 2
Business benefit:
•Given the body profile of a patient
and predicted level of disease , right
cure/medications can be suggested to
a patient
Business problem :
•A doctor/ pharmacist wants to predict
the likelihood of a new patient’s
disease being at
initial/intermediate/severe stage
based on various body attributes of a
patient such as blood pressure ,
hemoglobin level, sugar level , red
blood counts, TSH etc.
•Here the target variable would be level
of disease and would contain values
‘Initial, Intermediate and Severe’

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June 2018