Formulate and Interpret a Logistic Regression Model

Formulate and Interpret a Logistic Regression Model

Qualitative (categorical) dependent variables are dummy variables used as dependent rather than independent variables. Remember that a dummy variable is a variable that takes on the value 0 or 1. The logistic transformation takes the probability that an event happens, \(p\), divided by the probability that the event will not happen, \(1-p\). A logit is the natural logarithm of the odds of an event happening. The logistic transformation tends to linearize the relationship between the independent and dependent variables.

For example, suppose the probability of a company going bankrupt is 0.6, \(\frac {0.6}{ (1- 0.6)}=1.5\). In that case, the odds of a company becoming bankrupt are 1.5 times more than the probability of the company not going bankrupt. For this reason, we should use the logit model or discriminant analysis when estimating the probability of bankruptcy. The event probability can be calculated as follows:

If \(p\) is binary, we use the maximum likelihood method to estimate logistic regression coefficients instead of using least squares. The maximum likelihood method maximizes the likelihood function for the data. The Bernoulli distribution is chosen as the probability distribution because \(p\) is binary. The maximum likelihood method is iterative. Each iteration will result in a higher log-likelihood until the difference in the log-likelihood of two successive iterations is the same. At this point, the iterating process will stop.

Interpreting Logistic Regression Models

In a logit model, the slope coefficient is the change in the logit that the event happens per unit change in the independent variable. The exponent of the slope coefficient is the ratio of odds that the event will happen with a unit increase in the independent variable.

For a logit regression, the test of the hypothesis regression coefficient is significantly different from zero; it is the same as that of an ordinary linear regression. The overall performance of a logit regression can be evaluated by examining the likelihood chi-square test statistic.

Since logistic regression cannot be fitted using at least-square approach, logistic regression has no equivalent measure for the coefficient of determination. Researchers have proposed Pseudo − \(R^2\) to compare different specifications of the same model. However, it is unsuitable when comparing models with different datasets.


Which of the following measures is least likely to be used in interpreting a logistic regression model?

  1. R-squared.
  2. P seudo − \(R^2\).
  3. P-value.


The correct answer is A.

R-squared is not used because logistic regression cannot be fitted using a least-square approach.

B is incorrect. The Pseudo − \(R^2\) is used in logistic regression to compare different specifications of the same model, and it is an alternative for the R-squared.

C is incorrect. The p-value is used to evaluate the overall statistical significance of a model.

Reading 4: Extensions of Multiple Regression

Los 4 (c) Formulate and interpret a logistic regression model

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep

    Daniel Glyn
    Daniel Glyn
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    Crisp and short ppt of Frm chapters and great explanation with examples.