Linear Regression for Machine Learning Explained

Linear regression models are a fundamental topic in data science that falls into the category of machine learning. This type of machine-learning model is an incredibly fundamental model that is used very regularly through a variety of fields and has multiple applications, which can also be of a similar nature.

For example, the model can be used for either data prediction or data analysis, and given the breadth of these fields, we will be able to observe how incredibly useful and relevant this type of model can be to aid businesses with business insights or help forecast potential shortcoming or downturns of any industries.

Linear regression models generate huge amounts of value for a plethora of industries through the extraction of valuable insights that could save businesses millions of pounds, save businesses from the consequences of an economic recession, or help inform large-scale decision-making for heads of departments.

In this article, we shall be exploring the inner workings of linear regression models, how to create them, and provide you, as upcoming data scientists with the relevant knowledge you need to have a good understanding of how and why these models are important for all walks of life.

What do I need to know about linear regression? #

Linear regression is a form of machine learning model that is used for the purposes of statistical analysis and data analysis and allows us to model the relationship between two variables, known as the independent and dependent variable. This can be shown mathematically and through the use of coding. However, it is essential to understand the mathematics behind such models before delving deeper.

Linear regression can be displayed mathematically with the following notations:

This is the formula for a linear equation: ( y = mx + c )

• Y is referred to as the dependent variable. This is what we’re trying to predict.
• M represents the slope of the linear regression line in the model. Used to observe how much y will change when x changes by 1 unit.
• B represents the intercept. This will show us what our starting prediction will be when x = 0.
• X represents the independent variable. This is used to show how x impacts our prediction of y and their relationship.

When we take the values above and put them together inside a model what we then have is the linear regression model. This is known as a simple linear regression model because it models the relationship between one dependent variable and one independent variable.

However, we can also have what’s known as a multiple linear regression model. However, this is usually done when we are trying to examine and model the relationship between the dependent variable and multiple independent variables.

Ultimately, when examining the dataset you will be able to determine if the most appropriate will either be a simple linear regression model or multiple linear regression model.

This is because multiple linear regression models are usually more appropriate when you are provided with a dataset that has many variables that seem important and relevant to helping predict what the dependent variable is, and what the relationship between the dependent variable and multiple independent variables is.

What are some real-world applications of linear regression models? #

Linear regression models have many real-world applications. This is because any field that requires some degree of prediction and those fields can be within any of the fields listed below:

• Finance
• Economics
• Healthcare
• Real estate
• Sports analytics
• Energy and environment

A prime example of this could be Amazon attempting to predict what its future stock price is going to be. Therefore, the data analysts and data scientists at Amazon may attempt to use all the relevant available data and create a linear regression model to identify the relationships between different variables and stock prices.

Other factors included as independent variables could be variables such as seasonality, technological progress, brand image, and profits. This is because these factors may have some relationship with stock price and so it may be best to attempt to identify if a relationship is present and predict future stock prices based on these variables.

These types of models form the fundamental foundation for a whole variety of other algorithms because usually linear regressions or multiple linear regression models will be used to identify any relationships that are present between variables in the data and the further more complex machine learning algorithms will be deployed to extract deeper insights into the inner working of the dataset provided.

Being able to have ability to reflect on your findings for applying a simple linear regression or multiple linear regression will allow one to observe whether the increased complexity in the new models such as neural network models or logistic regression is justified in its efforts. Given that these models usually will attempt to build further upon the foundation of a linear regression model, with added complexity.

Assumptions of the linear regression model: #

Linear regression models also appear to have assumptions being made about either the relationships between variables inside the dataset or the data itself.

These assumptions are:

• Linearity between the variables. This means assuming there is a proportional change in Y for every change in X.
• Independence. This means that each piece of data should not be able to influence the others.
• Homoscedasticity. This means the variance of prediction errors should remain constant across different values of X.
• Normality. This would mean that the errors of the model should follow a normal distribution.

Therefore, any one of these issues could be violated by either the dataset or the relationship that is present between the variables. Financial datasets very oftenly violate the assumptions of independence because variables such as stock prices are influenced by their past values.

Thus, the most appropriate machine learning model to deploy depends on the assumptions of the model not being violated before deployment through thorough analysis of the nature of the dataset a Data Scientist must choose the model they deem most suitable for the job.

Summary: #

It is evident that linear regression models are a foundational machine learning model used throughout many domains of data science and data analytics, as these models can provide the foundation for more complex models and serve as a means of comparison. But, whether these models will be appropriate for use will depend on if the assumptions of the models are upheld or violated, as this will allow one to determine if this is the appropriate model to use to identify relationships between the variables and make predicts about the dependent variable, or not.

Also! #

If you enjoyed this article, please feel free to read my other articles where I regularly post about new data science topics and content to help inform you of the latest data science trends and foundational topics.

Have a great week ahead! 👋