LINEAR REGRESSION (In 7 Steps) (2024)

FAQs

What are the 7 steps in regression analysis? ›

Linear Regression Analysis consists of more than just fitting a linear line through a cloud of data points. It consists of 3 stages – (1) analyzing the correlation and directionality of the data, (2) estimating the model, i.e., fitting the line, and (3) evaluating the validity and usefulness of the model.

Linear regression models are known for being easy to interpret thanks to the applications of the model equation, both for understanding the underlying relationship and in applying the model to predictions.

Regression analysis seeks to establish a connection between a dependent variable and one or multiple independent variables, ultimately yielding a predictive equation. This process quantifies how alterations in independent variables influence changes in the dependent variable.

Linear regression models are relatively simple and provide an easy-to-interpret mathematical formula to generate predictions. Linear regression is an established statistical technique and applies easily to software and computing.

Interpreting Linear Regression Coefficients

A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also tends to increase. A negative coefficient suggests that as the independent variable increases, the dependent variable tends to decrease.

The strength of any linear regression model can be assessed using various evaluation metrics. These evaluation metrics usually provide a measure of how well the observed outputs are being generated by the model. The most used metrics are, Coefficient of Determination or R-squared (R2)

[1] To recapitulate, first, the relationship between x and y should be linear. Second, all the observations in a sample must be independent of each other; thus, this method should not be used if the data include more than one observation on any individual.

Why does linear regression fail? ›

This can be caused by accidentally duplicating a variable in the data, using a linear transformation of a variable along with the original (e.g., the same temperature measurements expressed in Fahrenheit and Celsius), or including a linear combination of multiple variables in the model, such as their mean.

Furthermore, linear regression is sensitive to outliers, meaning that a single extreme data point can significantly affect the slope and intercept of the line. In classification, outliers are common and might belong to either class, so we need a model that's more robust to such variations.

Regression analysis is essential for predicting and understanding relationships between dependent and independent variables. There are various regression models, including linear regression, logistic regression, polynomial regression, ridge regression, and lasso regression, each suited for different data scenarios.

Steps to Perform Regression Analysis:

Define the Problem: The first step is to define the problem and identify the variables that will be used in the analysis. Collect the Data: Collect data on the variables of interest. Check for Outliers: Identify and remove outliers, as they can skew the results of the analysis.