Linear regression

Linear regression is a form of predictive analysis with a wide variety of uses. When people are working with and analyzing unknown data, linear regression helps them use associated known data values to find similar, unknown data values.  

With the ability to associate value to a certain variable quickly, linear regression can be useful in many instances. Learn with Micron how and where linear regression is used, how it started and how it’s associated with artificial intelligence technologies.

What is linear regression?

Linear regression definition: Linear regression is a statistical method that models the relationship between a dependent variable and one or more independent variables to make predictions.

Linear regression uses simple mathematical formulas to generate predictions, making it a fundamental tool in predictive analysis. Within the broader artificial intelligence ecosystem, linear regression is grouped under the machine learning category because it’s a type of supervised machine learning algorithm that serves as a building block for more advanced machine learning models.   

Using linear regression in conjunction with artificial intelligence and machine learning models is a natural progress. Machine learning analyzes large datasets and can incorporate linear regression algorithms to enhance their predictive analysis capabilities. 

How does linear regression work?

There are three key stages of analyzing data with the linear model. The first step is to analyze any correlation between the data. The second step is to estimate the model, which often involves fitting a line to a scatter plot graph of the data. The third step is to evaluate the effectiveness of the method and determine whether the findings are valid.

Prior to these steps, various equations are used in the linear regression method. Each equation depends on the type of data and the complexity of both the data and the findings. 

The simplest linear regression technique works by attempting to plot a line graph between the x- and y-axes, establishing a relationship between these two variables.  

In this context, the x-axis represents the independent variable, and the y-axis represents the dependent variable, also known as the predicted variable. The y-axis values are determined by the x-axis values. 

What is the history of linear regression?

• 1800s, early development of the concept: The first iteration of linear regression was devised by Sir Francis Galton in the 19th century. This version of linear regression was a statistical mathematical model. 
• Late 1900s, modern application: As machine learning and artificial intelligence began to truly develop in the late 20th century, linear regression theories were applied to computers as a way of arriving at statistically probable results. Linear regression has since become fundamental to machine learning as a way of arriving at accurate predictive outcomes using mathematical models. 

What are the key types of linear regression?

Dealing with complex datasets requires different types of linear regression, with certain types being better suited for simpler datasets.

Simple linear regression is the simplest form of linear regression. The linear function of simple linear regression is represented by the following formula:

Y = β₁X + β₀ + ϵ   

where:

• Y is the dependent variable 
• X is the independent variable 
• β₀ is the slope 
• β₁ is the intercept
• ϵ is the random error component

Simple linear regression is typically used for determining the value of two datasets, hence the term “simple,” especially compared to other types of linear regression.

• Multiple linear regression builds on the foundations of simple linear regression. It involves two or more independent variables and one dependent variable to discover a relationship between them.
  
  It can also be used to determine the certain value of a dependent variable against the values of an independent variable, such as the blood pressure of someone based on age, gender, weight and other factors.

• The approach to logistic regression is slightly different from the other types of linear regression. While the main task remains analyzing the probability of an event occurring, the mathematical approach is different.

In logistic regression, the likelihood of an event happening is ranked between 0 and 1, with 0 indicating an unlikely event and 1 indicating a highly likely event. For example, logistic regression can be used to predict the probability of a specific outcome in sporting events.

How is linear regression used?

Given the versatile nature of linear regression and its practical applications, it is no surprise that there are plenty of use cases for this model. Even in its most basic form, linear regression can help provide accurate predictions, making it valuable in various fields such as business, finance, healthcare, education and many more.

Using linear regression as a tool for predictions in finance has stood the test of time and proven to be trustworthy. For example, the linear regression model can be used to predict the future profitability of a company. This ability can be particularly useful in the stock market to predict a business’s performance and prospects.

In the real estate industry, linear regression is beneficial in two main ways. First, it can help price a house by analyzing variables such as the location and size of the house. Second, it can predict a rise or fall in property prices. This approach again considers the variables of location, house size and current market for buying and selling properties.

Linear regression is also valuable in environmental science where it can provide insights into climate change by analyzing historical climate data and predicting future environmental impacts.