session pdf

8/10/2019 Session PDF

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Agenda for Coming sessions Analytics with Probabilistic Decision Making Model

Introduction to Logistics Regression

Decision Theory

Non Linear Models

Business Analytics and Application

Sentiment Analysis and Opinion Mining Online Business Channel and Web Analytics

Analytics in Marketing

Introduction to Markov Analysis Markov Decision Process

Poisson Process Models


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Continue Product Development

Introduction to Life Cycle Cost Total cost of ownership

Analytics In Operation

Introduction to Sig Sigma for problem solvingAnalytics In finance

Brownian Process

Asset Performance Measure


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Case Study 7i technology is a medium-sized consulting firm in San Francisco that

specializes in developing various forecast of product demand, sales,consumption, or other information for its clients. To a lesser degree, ithas also developed ongoing models for internal use by client companies.When contacted by a potential client, 7i technology usually establishes abasic agreement with the firms top management that sets out thegeneral goals of the end product, primary contact personnel in both

rms, an an out ne o t e pro ect s overa nc u ng any necessarytime constraints for intermediate and final completion and rough priceestimate for the contract). Following this step, a team of 7i personnel isassembled to determine the most appropriate forecasting technique andto develop a more detailed work program to be used as the basis for

final contract negotiations. This team which vary in size according to thescope of the project and the clients needs, will perform the tasksestablished in the work program in conjunction with any personnel fromthe client firm who would be included in the team.


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Continue Recently, 7i has been contacted by a rapidly growing multinational firm that

manufactures, sells android based tablets for enterprise and retail use.Honeycomb has seen aggressive in global and regional market and is in the

process to define new strategy to increase its present market share. But theproblem which the company is presently is facing is in terms of demand so thatthey can offer competitive price to increase their market share.

As a Business Analyst of 7i you must decide between different forecasting

approach. The linear trend equation is Yi= 12+2x, and it was developed using data from periods 1 through 10. Based

on the data from periods 11 through 20, calculate the MPE (Mean PercentageError) and MAPE (Mean Absolute Percentage Error).

Base on the values of MPE and MAPE comment on which of the two methods

has the greater overall accuracy. Compare the two methods in terms of theforecast bias.


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Data

11 2

12 2

13 3

1 0

1 3

1

1 0

1

20


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Since the MAPE values for the methods for the methods are

approximately equal, the overall accuracy of the two methods

is about the same. Both Methods are predicting

approximately 11 % away from actual.

-

trend equation is overestimating sales by 7.91%.

On the otherhand MPE is +ve for nave forecasting methods.

It is underestimating the sales by 7.66%


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Accuracy and Control


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Forecast Errors Forecast error is the difference between the value that occurs

and the value that was predicted for a given time period.

Error=Actual-Forecast

Positive errors results when the forecast is too low and


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Reasons of Forecasting errors The model may be inadequate due to (a) the omission of an

important variable, (b) a change or shift in the variable that the

model cannot deal with (e.g., sudden appearance of a trend orcycle), or (c) the appearance of a new variable (e.g., newcompetitor)

Irregular variations due to severe weather or other naturalp enomena, emporary s or ages or rea owns, ca as rop es, orsimilar events may occur.

The forecasting technique may be used incorrectly or the resultsmay be misinterpreted

There are random variations in the data. Randomness is theinherent variation that remains in the data after all causes ofvariation have been accounted for


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Types of Forecasting Accuracy Mean Absolute Deviation( MAD)

Definition: measures the average forecast error over anumber of periods, without regard to the sign of the error:

for computation, all errors are treated as positive.

Definition: the average squared error experienced over a

number of periods.


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Formula

== FAeMAD

( )

11

22

=

=

n

FA

n

e

MSE


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Continue The MSE is a variance, and the n-1 in its denominator is used

instead of n for essentially the same reason that n-1 is used to

compute a sample standard deviation model.

Difference Between the two models

,

more than the MAD measure.


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Monitoring and Controlling Forecast Is it time to reexamine the validity of the forecasting

technique being used?

There are two types of random errors

Which are inherent and cannot be removed from the model

econ one s non-ran om errors w c can e e m nate How to eliminate such errors?

Modifying the technique

Improving data collection .


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Forecast Error


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Mean Forecast Error (MFE)

FA

n

FE=


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The response variable, Y, is categorical


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Analytics In Decision Making Logistics Model

Introduction


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Quiz


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Difference Between Linear and

Nonlinear Regression Models

uiXiYi ++= 21

uiieYi Xi += 2Exponential Regression Model


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Business Problem in Marketing/ Retail What is the success probability by endorsing Chetan Bhagat

to promote Huwaie technologies products.

What channel of delivery is more effective.

What is the impact of price label on buyers decision.


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Business Problem in Banking and

Finance How to distinguish between good and bad credit risks.

How to identify most profitable customer.

How customer will react in terms of there invest in mutual

funds during bad market situations.


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Definition Logistic regression also known as logit analysis is a statistical

model used for prediction of probability of occurrence of an

event.

Logistic regression differs from multiple regression, however,

event occurring (i.e. the probability of an observation beingin the group). Although probability values are metric

measures, they are fundamental difference between two.


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What this model explains. Logistics Regression models how probability, P, of an event

may be affected by one or more explanatory variables.


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Classification Classifying customer by their buying habits between various

categories.

Classification by a telecom operators its various customers in

terms of usage.


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Challenger launch temperature vs

damage data


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Equation

Xe

Pi )(1

1

21 +

=+

ii

Z

Z

Zi

XZ

e

e

eP

i

21

11

1

+=

+

=

+

=


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Representation of Binary Dependent

Variable Logistic regression represents the two groups of interest as

binary variable with values of 0 and 1

The assignment of values is not important but the

interpretation of coefficient are done in this format

particular reason. The result would be success and failure.


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Use of Logistic Curve- Sigmoid or S

shaped

1012

1

0

2


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Explanation Binary Values has only value between 0 and 1

In order to define relationship in logistics regression we use

logistic curve between independent and dependent variable.


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Unique Nature of the Dependent

Variable Binary nature of the dependent variable (0 or 1) has

properties that violate basic assumptions multiple regression.

The error term of a discrete variable


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Logit Function The logit function is a logarithmic transformation of the

logistic function. It is defined as the natural logarithm of

odds.

Logit of a variable (with value between 0 and 1) is given

XInLogit10

1)(

+=

=


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Logistic Transformation The logistic regression model is given by

)(

)(

1 10

10

ee

iX

Xi

+

=+

+

110

)(

1

1

10

XIn

e iX

i

i

+=

=

+


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More robust

Error terms need not be normal

No requirement for equal variance for error terms

No requirement for linear relationship between dependent

an epen ent an n epen ent var a es.


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In standard regression , the error term is assumed to follow

normal distribution whereas in case of logistics regression its

not the same.

In case of binary logistics regression, the error for a given

-

.


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Estimation of parameters No closed form solutions exists for estimation of regression

parameters of logistics regression.

Estimation of parameters in logistic regression is carried out

using Maximum Likelihood Estimation (MLE) technique.

M i Lik lih d E ti t r


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Maximum Likelihood Estimator

(MLE)


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MLE is a statistical model for estimating model parameters of

a function

For a given data set, the MLE chooses the values of the

model parameters that makes the data more likely than


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E.g. Exponential Distribution Let x1, x2, , xn be the sample observation that follows

exponential distribution with parameter .

That is:

f(x, )=

The likelihood function is given by (assuming independence):

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