Regression Analysis - Logistic vs. Linear vs. Poisson Regression

Regression Analysis enables businesses to utilize analytical techniques to make predictions between variables, and determine outcomes within your organization that help support business strategies, and manage risks effectively.

Regression analysis involves certain parameters and variables: unknown variables, independent variables, and dependent variables. It also encompasses three distinctive types of regression models:

  • Linear
  • Logistic
  • Poisson

To utilize data most effectively, and ensure that it can be applied toward deriving the right types of insights, organizations can apply these three forms of Regression Analysis. These regression models help in finding answers to vital business questions. The main uses for this type of analysis are causal analysis, forecasting events, and trend forecasting.

Linear Regression

Linear regression is the most simplistic form of regression, utilized to evaluate a relationship between two variables, and is particularly useful for analyzing risk. A business might apply linear regression to determine that if there's an increase in demand for a product; production would have to increase at the same rate, demonstrating a linear relationship between these two figures.

For example, if a business decides to alter the price on a specific product several times, the price for quantity sold can be recorded, and a Linear Regression can be performed with quantity sold as the dependent variable, and the price as the explanatory variable.

It uses the mathematical formula of a straight line:

y = mx + b

Meaning a graph with the Y and X axis would indicate the relationship between X and Y as a straight line with minimal deviation.For example, a healthcare insurance company can analyze the number of claims per customer age brackets. You can determine that older customers make more insurance claims. This type of analysis can support crucial business decisions that factor in specific risks.

Logistic Regression

Logistic Regression is a binary form of classification and represents outcomes that are pass/fail, or win/lose, for example. The main objective is to locate the most suitable model to characterize the relationship between the dichotomous character of interest, and a set of independent (predictor or explanatory) variables.

Logistic Regression is as follows:

  • It only contains data coded as either 1 (True/Success), or 0 (False/Failure).
  • The dependent variable is binary and surmises that the dependent variable is a randomly determined event.

For example, businesses may want to forecast the likelihood of a new service or product being successful upon launch. Or if their sales have been steadily increasing every month over the last year, a Logistic Regression analysis can be used to forecast sales for upcoming months based on a linear analysis of the monthly sales data. More generally, it's an ideal option for evaluating trends and making estimates and predictions.

Poisson Regression

Poisson Regression is the best option to apply to rare events, and it is only utilized for numerical, persistent data. It describes which explanatory variables contain a statistically consequential effect on the response variable. Simply speaking, it tells businesses which X-values work on the Y-value.

The model for Poisson Regression is as follows:

Here is a simple formula of the equation with one dependent and one independent variable:

y = c + b*x

Assumptions for this type of regression analysis include:

  • Y-values are the counts: Poisson regression is not the right method if your response variables are not counts
  • Counts have to be positive integers: You cannot use negative numbers or fractions because this is a discrete distribution
  • Poisson distribution must be followed by Counts: The variance and the mean have to be the same
  • Explanatory variables have to be continuous, dichotomous or ordinal
  • Observations must be independent

For example, an insurance company can apply Poisson Regression toward determining the claims for policyholders based on car types, driver ages, and other predictor variables, such as driver gender or occupation.

Regression Analysis to Suit All Business Needs

Companies can utilize Regression Analysis to effectively and accurately predict trends and events, evaluate risks, and support decision-making strategies. Research Optimus (ROP) provides professional, advanced statistical modeling and regression analysis services for businesses of all sectors that are designed to address the personalized needs of a wide variety of industries and businesses. To know more about our services,

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