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Analytics using SAS © Beacon Learning
Regression Models
Analytics using SAS © Beacon Learning
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%?
Analytics using SAS © Beacon Learning
Simple vs multiple Regression
Define Y
Identify X
Estimate
Interpret
uxxxy kk ....22110
Analytics using SAS © Beacon Learning
Non Linear Probability Models
ktiit Xfp ,
Analytics using SAS © Beacon Learning
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
Analytics using SAS © Beacon Learning
Problems with LPM
Goodness of Fit
Improbable Probability Estimates
Linear Incremental Effect of variables on Default Probability
Analytics using SAS © Beacon Learning
Goodness of Fit
Analytics using SAS © Beacon Learning
Improbable Probability Estimates
Linear Incremental Effect of variables on Default
Probability
Other Problems with LPM
Analytics using SAS © Beacon Learning
How should it look like?
Analytics using SAS © Beacon Learning
Non Linear Probability Models
Linear vs Non Linear Regression
Logit Model
Probit Model
Analytics using SAS © Beacon Learning
Logistic Model (Logit Models)
k
jij
k
jij
e
eP
10
10
1
Analytics using SAS © Beacon Learning
Linear Transformation
k
j
ij
i
i
iP
PL
1
01 ln
Log-Odds Ratio
Analytics using SAS © Beacon Learning
How does the probability change?
)1( PPdx
dPj
j
Analytics using SAS © Beacon Learning
Estimation and Interpretation
01
1
ii y
i
y
i PP
Maximum Likelihood Technique
Likelihood function
.Choose j to maximize
Analytics using SAS © Beacon Learning
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%
Analytics using SAS © Beacon Learning
Probit Model
Analytics using SAS © Beacon Learning
Logit versus Probit
