Calculating Linear vs. Logistic Regression: Definitions and Steps

By Indeed Editorial Team

Published July 27, 2021

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In machine learning, linear regression and logistic regression encompass supervised learning processes that programmers use to develop interactive and responsive systems. When computing linear regression, you can calculate a regression line that shows the predictive relationship between a random input and desired output. Conversely, logistic regression can give you insight into classification problems. In this article, we explore what linear and logistic regression models are, how to calculate both types of regression and when to convert linear to logistic regression.

What is linear regression?

Linear regression is a statistical approach to creating a linear model that predicts the continuous relationship between a dependent and independent variable. This relationship between variables elicits a scalar response, from which analysts and statisticians can gather information about a sample or population. When a linear regression model includes only one causative or independent variable, it remains a simple linear regression.

When a model contains multiple explanatory variables, the process becomes a multiple linear regression. In mathematical terms, linear regression expresses as a linear equation, where a dependent variable is a function of an independent variable. When calculating simple linear regression, this equation shows up as a line that represents the changes in variables.

Read more: Linear Regression: A Definitive Guide

What is logistic regression?

Logistic regression uses linear regression to compute machine learning results that have only two outcomes, making this regression model a binary analysis method. It predicts the probability of an outcome and is essential in supervised machine learning. Unlike a linear regression model, a logistic regression model uses a set of independent variables to determine the probability of change or an event occurring.

This process results in two dependent variables because these values remain constant or can only change according to the influence of the independent variables. When computing this regression model, the independent variables can be continuous and represent infinite values, discreet ordinal and finite variables in ranking order or discreet nominal and finite variables without a ranking order.

Related: Regression Analysis: What It Is and How To Use It

Calculating linear vs. logistic regression

Both linear and logistic regression models are necessary for regression analysis across a range of applications. In addition, logistic regression relies on the regression line you derive from a linear model in order to gain its binary results. However, there are some differences when calculating the two values. Use the following steps to compute linear regression and logistic regression and see how the two models correlate with one another:

How to calculate linear regression

Because linear regression models use lines to represent the rate of change and statistical relationships between inputs and outputs, this model uses a linear equation. To derive linear regression values, you can use the formula:

Y(x) = mx + C

In the formula, "Y" is a dependent variable and a function of "x," which represents the independent or explanatory variable. You can use the following steps to apply the formula to calculate linear regression:

  1. Determine input values for x. When constructing the linear regression model, let x represent the input value. For instance, if a software developer wants a certain output (Y in the equation), they use the x variable to represent the input value, such as inputting specific code that tells a system to generate a functional output.

  2. Assign the gradient to the m value. The gradient value represents the slope of the line of the regression model and measures the rate at which the dependent variable changes based on the independent variable.

  3. Substitute the constant for C. The C variable is the constant value in your algorithm that remains the same throughout the linear regression model. In machine learning, a constant can be predictive values programmers use to achieve outputs when calculating linear regression with different inputs.

  4. Compute the linear regression equation. Once you have your variables and predictive values, you can compute the entire equation to find the linear regression model, which gives you a straight line. Using this information, programmers who develop and design machine learning systems can then analyze the functionality, activation and supervised learning efficiency of various artificial intelligence networks.

Related: Multiple Regression Analysis: Definition and How To Calculate

How to calculate logistic regression models

Logistic regression focuses on determining a probability threshold that dictates a reasonable range where dependent variables can show up. Since logistic regression analysis gives binary results, the equation to compute this value differs from the linear regression equations and computation processes.

You can apply the sigmoid equation to calculate logistic regression:

S(x) = 1 / (1 + e-x)

In this formula, x represents the input value, and the S variable is a function of x. The e value represents the predictive error value that the mean squares method of linear regression uses when determining the accuracy of predictive analysis. To calculate logistic regression from a linear regression model, use the following steps to apply the formula:

  1. Use the regression line from the linear model. When you compute a regression line, you can convert this predictive value into a logistic regression model that provides a probable outcome between zero and one.

  2. Assign the linear regression values to the sigmoid function. Using the x value and the residual error (e) from your linear regression model, plug these values into the sigmoid equation.

  3. Convert the sigmoid value to a one or zero. Once you derive the logistic regression value from the sigmoid function, you can convert this value to a one or zero, depending on where the value appears on an S-curve. For instance, if the logistic regression results in a value of 0.78, you can convert this to a one to represent the closest discrete value.

Read more: Logistic Regression vs. Linear Regression: What's the Difference?

When to convert linear to logistic regression

Converting a linear to a logistic regression model can be necessary when applying binary classification to a sample data set. Binary classification occurs when you create a parameter to classify sample data into two distinct categories. In supervised machine learning, converting linear regression to logistic regression is necessary for solving classification problems when analyzing the residual error of a regression line. Consider several more instances when it's applicable to convert linear to logistic regression:

  • Evaluating the proportion of profits to losses in sales

  • Analyzing the effects on symptoms during pharmaceutical studies

  • Measuring the customer churn rates in marketing

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