Simplifying stats

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Regression Models

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Regression

Predictive Modeling

Which Factors Explain?

Regressive vs. Correlation

Examples:

What will be India’s Energy Consumption as GDP grows by 6.5%?

What is the probability that a customer will default on housing loan

How many fatal road accidents will you have in Delhi if the traffic

volume increases by 10%?

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Simple vs multiple Regression

Define Y

Identify X

Estimate

Interpret

uxxxy kk ....22110

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Non Linear Probability Models

ktiit Xfp ,

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Linear Probability Model (LPM)

uxxxp kk ....22110 …….

where, p

kxxx ,...,, 10

is the probability of default

kare the explanatory variables

.

yRegress an indicator variable on kxxx ,...,, 10

y is a dichotomous variable with possible values

defaultednot has firm theif 0

defaulted has firm theif 1y

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Problems with LPM

Goodness of Fit

Improbable Probability Estimates

Linear Incremental Effect of variables on Default Probability

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Goodness of Fit

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Improbable Probability Estimates

Linear Incremental Effect of variables on Default

Probability

Other Problems with LPM

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How should it look like?

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Non Linear Probability Models

Linear vs Non Linear Regression

Logit Model

Probit Model

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Logistic Model (Logit Models)

k

jij

k

jij

e

eP

10

10

1

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Linear Transformation

k

j

ij

i

i

iP

PL

1

01 ln

Log-Odds Ratio

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How does the probability change?

)1( PPdx

dPj

j

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Estimation and Interpretation

01

1

ii y

i

y

i PP

Maximum Likelihood Technique

Likelihood function

.Choose j to maximize

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Goodness of Fit: Concordant Analysis/Specificity vs Sensitivity

Estimated

Equation

Actual Won Lost Total

Predicted

Won 160 61 221

Lost 133 1345 1478

Total 293 1406 1699

Correct 160 1345 1505

% Correct 54.6 95.7 88.6

% Incorrect 45.4 4.3 11.4

Constant

Probability

Won Lost Total

0 0 0

293 1406 1699

293 1406 1699

0 1406 1406

0.0 100.0 82.8

100.0 0.0 17.2

Sensitivity 54.61%

Specificity 95.66%

Positive predictive value 72.40%

Negative predictive value 91.00%

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Probit Model

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Logit versus Probit