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A Beginner’s Guide to Regression Analysis

Published by at September 1st, 2021 , Revised On July 5, 2022

Are you good with data-driven decisions at work? If not, why? What is stopping you from getting on the crest of a wave? There could be just one answer to these questions, and that is “too much data getting in the way.” Do not worry; there is a solution to every problem in this world, and there is definitely one for parsing through tons of data.

Yes, you heard it right! You will not have to get in trouble with the number crunching and counting with this solution. What is the solution?

Well, without further ado, we would like to introduce you to “regression,” which precisely is allowing one to see into the future.

What is Regression Analysis?

Here is a scenario to help you understand what regression is and how it helps you make better strategic decisions in research.

Let’s say you are the CEO of a company and are trying to predict the profit margin for the next month. Now you might have a lot of factors in your mind that can affect the number. Be it the number of sales you get in the month, the number of employees not taking leaves, or the number of hours each worker gives daily. But what if things do not go as planned? The “what if” list here has no stop; it can go on forever.  All these impacting factors here are variables, and regression analysis is the process of mathematically figuring out which of these variables actually have an impact and which are not plausible.

So, we can say that regression analysis helps you find the relationship between a set of dependent and independent variables. There are different ways to find this relationship between variables, which in statistics is named “regression models.”

We will learn about each in the next heading.

Types of Regression Models

If you are not sure which type of regression model you should use for a particular study, this section might help you.

Though there are numerous types of regression models depending on the type of variables, these are the most common ones.

  • Linear Regression
  • Logistic Regression
  • Ridge Regression
  • Lasso Regression
  • Polynomial Regression
  • Bayesian Linear Regression

Linear Regression

Linear regression is the real workhorse of the industry and probably is the first type that comes to mind. It is often known as Linear Least Squares and Ordinary Least Squares. This model consists of a dependent variable and a predictable variable that align with each other. Hence, the name linear regression. If the data you are dealing with contains more than one independent variable, then the linear regression here would be Multi-Linear Regression.

Logistic Regression

Logistic Regression comes into play when the dependent variable is discrete. This means that the target value will only have one or two values. For instance, a true or false, a yes or no, a 0 or 1, and so on. In this case, a sigmoid curve describes the relationship between the independent and dependent variables.

When using this regression model for the data analysis process, two things should strictly be taken into consideration:

  1. Make sure there is no multi-linearity (like that in the linear regression model) or correlation between the two variables in the dataset
  2. Also, ensure that the size of data is big with the equal manifestation of values to come in targeted variables

Ridge Regression

When there is a high correlation between the independent and dependent variables, this type of regression is used. It is simply because, with multi collinear data, least-square estimates give impartial numbers. However, if the collinearity is high, there might be a slight chance of unfair judgment.

Thus, a bias matrix is brought to the surface in ridge regression. This powerful type of regression is less vulnerable to overfitting. Are you familiar with the ‘overfitting’ word?

Overfitting in statistics is a modeling error that one makes when the function is too closely brought into line with limited data points. When a model in research has been compromised with this error, it might lose its value all at once.

Lasso Regression

Lasso Regression is best suitable for performing regularization alongside feature selection. This type of regression hinders the absolute size of the regression coefficient. What happens next? The coefficient value will almost come nearer zero, which the complete opposite of what happened in Ridge Regression.

This is why feature selection utilizes this regression model that helps to select a set of features from the dataset. Only required and limited features are used in Lasso Regression, and all the other features are zero. Researchers get rid of the overfitting in the model by doing this. But what if the independent variables are highly collinear?

In that case, this model will only choose one variable and turn the others to zero. We can say that it is somewhat like the Ridge Regression but with variable selection.

Polynomial Regression

This is another type of regression that is almost the same as Multi-Linear Regression but with some changes. In the Polynomial Regression Model, the relationship between the two variables, dependent and independent, is denoted by the nth degree. While in a Multi-Linear Regression Model, the line is linear, here it is the opposite. The best fit line in Polynomial Regression passing through all the points is curved. This curve either depends on the value of n or the value of X.

This model is also prone to overfitting. It is best to assess the curve towards the end as the higher polynomials might give strange and unexpected results on extrapolation.

Bayesian Linear Regression

The last type of regression model we are going to discuss is the Bayesian Linear Regression. Have you heard of the Bayes theorem? Well, this regression type basically uses that to figure out the value of regression coefficients.

It is a lot like both Ridge Regression and Linear Regression, but the stability here is much higher. In this model, we find the value of the posterior distribution of the features instead of working on the least squares.

FAQs About Regression Analysis

It is a technique to find out the relationship between the dependent and independent variables

Linear Regression Model helps determine the relationship between different continuous variables by fitting a linear equation for dealing with data.

The only difference between Multi-Linear Regression and polynomial repression is that in the latter relationship between ‘x’ and ‘y’ is denoted by the nth value, so the line here is a curve. While in Multi-Linear, the line is straight.

When a function in statistics corresponds too closely to a particular set of data, some modeling error is possible. This modeling error is called overfitting.

It is a method of finding the coefficients of multiple regression models in which the independent variables are highly correlated. In other words, it is a method to develop a parsimonious model when the number of predictable variables is higher than the observations in a set.

About Owen Ingram

Ingram is a dissertation specialist. He has a master's degree in data sciences. His research work aims to compare the various types of research methods used among academicians and researchers.