Linear Regression Implementation in Python: A Complete Guide

Whether you’re studying machine learning or statistics with Python, you would come across linear regression. Linear regression is one of the machine learning certification course’s important part. 

What is it? How do you perform linear regression with Python?

In this article, we’ll be discovering answers to these questions. After reading this article, you’d become familiar with:

  • Regressions and what are they
  • What is linear regression
  • How to train a linear regression model
  • Applications of linear regression

Let’s get started. 

What is Regression?

Regression analysis refers to specific statistical processes that you use for estimating the relations between a dependent and an independent variable.

It is popular in multiple industries, such as finance and banking. By using regression analysis, you can understand the relationship between two variables in a specific environment. 

Suppose you want to find the prices of houses in a particular area. For that purpose, you will need to observe the city of the area, number of residents, availability of amenities, and many other things.

The things on which the houses’ prices will depend on are called features. And the problem where the factors are related to the cost of each home is an observation. In this example, the presumption is that the location, amenities, and other factors affect the price of each home. 

In simpler terms, you make a few observations regarding a particular subject in regression analysis. Your observations have a few features and some presumptions before you start forming a relationship among them. 

There are two kinds of features in the regression analysis. They are:

  • Dependent features, which are called dependent outputs, variables, or responses
  • Independent features, which are called independent outputs, variables, or responses

Generally, a regression problem has one continuous dependent variable. The inputs vary. 

You can denote the outputs with y and inputs with x. There are no hard and fast rules for it, but it’s a general practice to use y and x for denoting these output and input. 

If you have multiple independent variables, you can represent as x = (x1,…,xr), where r denotes the number of inputs. 

What is a Linear Regression?

Linear regression is the most popular type of regression. It is a statistical method to model relationships between a dependent output and a group of independent outputs. 

In this article, we’ll call independent outputs ‘features’ and dependent outputs ‘responses’. 

If a linear regression only has one feature, it is called Univariate linear regression. Similarly, if it has multiple features, you’d call it Multiple linear regression.  

The most notable advantage of linear regressions is the ease of interpreting their results.  Linear Regression Interview Questions

It is the simplest form of regression. 


If y is the predicted value, 0 is the bias term, xn and are the feature values, and you’d represent the linear regression model by the following equation:

Y = 0 + 1x1 + 2x2 +…. +nxn 

Here n denotes the model parameters. 

Linear Regression Python Code

To create a linear regression model, you’ll also need a data set to begin with. There are multiple ways you can use the Python code for linear regression.

We suggest studying Python and getting familiar with python libraries before you start working in this regard. 

It can help you create a basic linear regression model. 

Training the Regression Model

You will have to find the necessary parameters for the model, so it best fits the data. You will have to find the best fit line (or the regression line). 

The regression line is the one for which the error between the observed figures and the predicted figures is the minimum. Another name for these errors is residuals. 

For measuring the error, you’ll have to define the cost function:

J () = 12m i=1m(h(xi) – yi)2

Here, h(x) stands for hypothesis function, which is denoted by the equation we discussed before:

h(x) = 0 + 1x1 + 2x2 +…. +ixi

m stands for the total number of examples in our data set. 

Using these equations and an optimization algorithm, you can train your linear regression model. 

There are many other methods of performing Python regression analysis, which we’ve discussed below:

Performing Linear Regression with Python Packages

You can use NumPy, which is a widespread and fundamental Python package. It is used for performing high-performance operations. It is open-source and has many mathematical routines available. 

You can check out the NumPy user guide for finding out more information about it. You’d need to learn about scikit-learn as well, which is a popular Python library based on NumPy. It is popularly used for machine learning and similar activities. 

For developing linear regression models and implementing them, you should also learn about statsmodels. It is another powerful Python package, which is used for performing tests and estimating statistical models. 

What are the Applications of Linear Regression?

Linear regression finds uses in many industries. Here are a few applications of linear regression:

1) Understanding Trends

Linear regression can help companies in understanding market trends. This way, they can plan their strategies better and avoid making mistakes. Apart from companies, traders, as well as, research organizations can also use this technique for evaluating trends. 

2) Analyzing Price Changes

Price changes in commodities can have a significant impact on the profits of produce businesses. Linear regression can help companies with this task, too, as they can find relations between the price changes and the factors contributing to them. 

3) Risk Assessment

Insurance companies, as well as investors, can use linear regression to find out anomalies. Investors can find their weak investments and plan out their strategies accordingly while reducing risk. 

Concluding Thoughts

Linear Regression is one of the important AI algorithms and we hope you found this guide on linear regression with Python useful. Python regression can be quite daunting for a beginner. That’s why we recommend getting familiar with Python packages and algorithms first. 

Knowing about those two alone will benefit you greatly in implementing linear regression. 

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