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# Simplifying stats

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### Simplifying stats

1. 1. Analytics using SAS© Beacon Learning Regression Models
2. 2. 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%?
3. 3. Analytics using SAS© Beacon Learning Simple vs multiple Regression Define Y Identify X Estimate Interpret uxxxy kk   ....22110
4. 4. Analytics using SAS© Beacon Learning Non Linear Probability Models  ktiit Xfp  ,
5. 5. 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     defaultednothasfirmtheif0 defaultedhasfirmtheif1 y
6. 6. Analytics using SAS© Beacon Learning Problems with LPM  Goodness of Fit  Improbable Probability Estimates  Linear Incremental Effect of variables on Default Probability
7. 7. Analytics using SAS© Beacon Learning Goodness of Fit
8. 8. Analytics using SAS© Beacon Learning  Improbable Probability Estimates  Linear Incremental Effect of variables on Default Probability Other Problems with LPM
9. 9. Analytics using SAS© Beacon Learning How should it look like?
10. 10. Analytics using SAS© Beacon Learning Non Linear Probability Models  Linear vs Non Linear Regression  Logit Model  Probit Model
11. 11. Analytics using SAS© Beacon Learning Logistic Model (Logit Models)       k j ij k j ij e e P 1 0 1 0 1  
12. 12. Analytics using SAS© Beacon Learning Linear Transformation     k j ij i i i P P L 1 0 1 ln   Log-Odds Ratio
13. 13. Analytics using SAS© Beacon Learning How does the probability change? )1( PP dx dP j j  
14. 14. 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
15. 15. 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%
16. 16. Analytics using SAS© Beacon Learning Probit Model
17. 17. Analytics using SAS© Beacon Learning Logit versus Probit