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Logistic Regression

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What is logistic regression? Explain logistic regression formula with an example?

First before understanding what Logistic Regression let is us understand where this concept is used in rigorously.

Have you ever tried to predict the result of a match, or which team will win the world cup?

If yes, then you would be thinking how big media houses and betting houses decide on the rate of win or loss.

Well, as it turns out all of this is no Voodoo magic but a simple statistical tool called logistic regression or logit regression.

I am sure now this concept relates to you with real-time examples where you are closely associated to.

Now, let us understand what Logistic Regression is in detail:

It is a very common process where the dependent variable is categorical or binary, that is the dependent variable or in lay man’s terms, the result is either a yes or no.

Logistic regression is one of the types of regression model where the regression analysis is executed when the dependent variable is binary. This regression method is used to explain the data and the relationship between the independent binary variable and one or more nominal, ratio-level independent variables.

Developed by statistician David Cox in 1958. The risk factor, in this case, affects the end result in a very emphatic way.

So now we understand that this regression method is based on data and it helps the individual to make some predictions.

So wondering where these predictions are used.

Well, some of the predictions are listed below for your in-depth understanding:

  1.  It has vast use in the field of medical statistics where it helps determine whether a person has a given disease or not.
  2. This is used for diseases like diabetes and coronary heart diseases.

  3. The election predictions are also based on the same regression logic.

  4. Whether an American would vote for a republican or democratic is also determined by the same procedure taking in demographic variables.

  5. It is used by economists and even bankers to determine if a person will default the loan or not.

So Logistic Regression analysis is used to determine the behavioural pattern of an individual?

Well yes, the logistic regression analysis is widely used to determine the behavioural pattern of the individuals where they are able to predict an outcome. Most of the time the outcome can be either yes or no. This regression analysis is widely used in each and every organization and based on the prediction made the decisions vary. Thus impacting the overall execution of the day to day process in an organization.

It can also be used as a risk analysis tool.

Logistic Regression Formula:

The logistic regression formula is far more complex than a normal regression formula and requires special training and practice to master. This is a subtle art and specialists are often difficult to find. The data set in this case needs to be more accounting to the huge complexity of the issue. Here also the issue of multi-collinearity needs to be taken care of due to its huge impact on imposing biases.

The formula above shows the probability of an event occurring and is determined on the basis of conditional probability and binomial theorem.

Example:

A research was done to find the impact of hours studied on the passing and failing of student to determine the probability of both the cases. The analysis was done on a set of students and the following data was recorded.

Based on this data the logistic regression was done and the following results were found out -

The intercept was found to be at -4.0777 with a standard error of 1.7610 while the hours coefficient was found to be at 1.5046 with a standard deviation of 0.6287. This hours coefficient of 1.5046 is the regression proportionality factor in this case. The probability of pass or fail was found out using the listed formula as follows-

Probability formula

The final result was found to be –

logistic regression - Analysis result

Thus it was found that a student studying 1 hour has 7% chance of passing while studying for an hour more increases his chances of passing incrementally to 26%. Similarly studying for 3 hours increases the probability to 61%, but from here on the chances flattens down as studying for 4 hours gives a chance of 87% and for 6 hours increases it to 97%. Thus a student studying for more than 5 hours a day it is almost certain to pass.

Conclusion:

In today’s article, we discussed on logistic regression model and its uses. This is a vital analysis model for the organizations where it helps the business owners to take appropriate decisions based on the predictions made. This model is widely used in different areas of the business and mainly used to understand the behaviour of an individual, i.e. it can be buying pattern of an individual, it may the way the individual is using a particular choice/option etc.

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