Education

# What is Linear Regression?

Looking at the applications like Alexa (voice assistant), driverless cars, email spam filtering, and recommendation engines in e-commerce websites, you must be fascinated by machine learning – a technology that powers all of them. In fact, if you are an IT professional, then you may tend to switch to a machine learning field. And why not? It is one of the fastest-growing career domains, along with lucrative salary prospects. Today, it is common to see professionals enrolling in a Machine learning basics program so as to gain the right skills and pave their way towards starting a promising career.

Basically, machine learning is a subset of artificial intelligence that aims to provide computer systems the ability to learn from experience and improve on their own, just like humans. The process involves training a system with relevant input data so that it can identify patterns and provide desired results. Multiple iterations of learning are carried out so that the errors are reduced, and the system gives accurate output. A number of machine learning algorithms are used for this purpose. When diving more into such algorithms, you will come across a popular algorithm called Linear Regression.

This article explores what linear regression is all about and why you should be familiar with it.

Contents

## Linear Regression Explained

You must know that machine learning is generally of three types – supervised learning, unsupervised learning, and reinforcement learning. Supervised learning is associated with a training set that is used to teach a system to generate the desired output. In other words, the training dataset includes input values mapped to their correct output values. This labeled dataset trains the model so as to classify data or predict outcomes correctly. A variety of computational techniques are used for the supervised machine learning process, and one of them is Linear Regression.

When we have to make predictions about future outcomes, we make use of Linear Regression. It basically involves determining the relationship between a dependent variable and one or more independent variables. This relationship is found by plotting a line that fits the input data and maps it onto the output. The method of least squares is used to calculate the line of best fit. This type of regression can be used to identify the effect of input variables on target variables or the change in target variable with respect to input variable(s).

You must have solved equations in linear algebra that involved x and y values, generally a quantitative response ‘y’ from the predictor variable ‘x’. Mathematically, here is how the linear regression equation is written:

y = a + bx

where, x and y are two variables on the regression line, b is the slope of the line, and a is the y-intercept of the line. As you can see, x is the independent variable and y is the dependent variable. This equation represents simple linear regression as it involves only one independent/input variable. When there are more than one input variables involved, it is called multiple linear regression.

The following image shows a simple linear regression curve for the above equation:

The line of regression shown above can represent either a positive linear relationship or a negative linear relationship. If the dependent variable ‘y’ increases with the value of independent variable ‘x’, then it is a positive relationship. On the other hand, if the value of ‘y’ decreases with the increasing value of ‘x’, then it is a negative linear relationship.

Estimating the values of the coefficients (‘a’ and ‘b’ in the above equation) used in the representation with the available data is called learning a linear regression model. As mentioned earlier, we use the method of Ordinary Least Squares to estimate the values of these coefficients. The OLS methods works by minimizing the sum of the squared residuals. As shown in the above image, there are many data points. So, in OLS, we calculate the distance of each data point from the line of regression, square them, and get the sum of all the squared errors together. It is as shown below:

Here, it is important to note that when conducting a linear regression, it is always assumed that the line of regression is a straight line. It doesn’t involve any curve or grouping factor as it is a parametric test.

## Why Learn Linear Regression?

Professionals familiar with statistics must already be using linear regression. For business, linear regression can be used to predict the sales of a product, its pricing, risk, performance, etc. It is considered a powerful statistical technique that can be leveraged to generate actionable insights on consumer behavior, factors that affect profitability and make estimates or forecasts. With a better understanding of the business, linear regression can also help analyze the marketing effectiveness, pricing, and promotions on the sales of a product.

Linear regression has various other applications in different industries. For the insurance and banking sector, it can be used for risk assessment. In agriculture, experts can predict the yield of the crop based on the amount of rainfall that occurs. For corporates, this statistical technique can be used to predict the salary of an employee based on the years of experience they possess. With so many applications, it is wise to learn using linear regression, especially if you are starting a career in machine learning.

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