Logistic Regression
In the previous session, we discussed in detail the concepts and the principles underlying Linear Regression. In this session we will understand the methodology associated with Logistic Regression.

Logistic regression is in many ways similar to Linear Regression. Linear Regression allows us to model the relationship between a dependent and one or more independent variables. We can also view the goodness of fit of the model as well as the significance of the relationships that we have been modelling using Linear Regression.

However there is a difference in the underlying principles of Logistic Regression and Ordinary Linear Regression. We are now aware that Linear Regression uses Ordinary Least Squares to find the best fitting trend line and subsequently coefficients are found out which predicts changes in dependent variable based upon a unit change I the independent variable.

This is unlike Logistic Regression, where the output is not the trend line or coefficients (Linear Regression) but the estimates of probability of an event lying between 1 & 0.

Hence, while in Linear Regression, we assume that the relationship between dependent and independent variables is linear, it is not so in the case of Logistic Regression.

Why to use Logistic Regression instead of Linear Regression?
• While using Linear Regression, if you move too far on the X-axis, the predicted values will be greater than one and less than zero. This could pose problems for subsequent analysis.
• One of the assumptions of Linear Regression is the presence of homoscedasticity (i.e variance of Y is constant across different values of X).This is not true in case of a binary variable.
• The error terms are not normally distributed.

Sample Case Study on Logistic Regression

Suppose there is researcher who wants to know what factors/variables influence the admission process into an MBA programme in Cambridge University.
After detailed research, he came out with the following three most influential factors:

1) GRE (Graduate Record Examination) Scores (GRE)
2) GPA (Grade Point Average) obtained in graduation (GPA)
3) Prestige of the Graduate Institution/ Ranking of the institution (RANK)

The above three variables are the predictor variables in the regression and the response variable is admit/don’t admit is a binary variable.

Now you can run Logistic Regression on the data to find out the logistic regression coefficients which give the change in log odds of the outcome for a unit increase in the predictor variables (GRE, GPA, RANK).

Please note that we cannot use Linear Regression here because the response variable is a Binary variable unlike a continuous variable in case of Linear Regression.

Running Logistic Regression Using R

Excel cannot compute Logistic Regression and hence we useR statistical package/software to run Logistic Regressions. This is due to the following drawbacks in excel:

• Excel does not handle categorical predictors.
• Output in Excel may be incomplete or may not be properly labelled,thus increasing possibility of misidentifying output.
• We need to repeat requests for some analyses multiple times in order to run it for multiple variables, or to request multiple options.

Below we can see a snapshot while running Logistic Regression using R:
Scorecard Development

• So, from the above discussion, we now know that the output of Logistic Regression is in the range of (0,1). These results are then used by risk managers to select/reject customers or by management to take strategic decisions etc.
• However, before the Logistic Regression output is used for further analysis, it has to be mapped to a more readable format.
• Thus, the output is transformed into a set of scores, also referred to as the Scorecard.
• A properly transformed scorecard produces the same result as obtained from fundamental model output.

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