The data analytics job market is thriving as data becomes increasingly important in corporate decision-making. As per Gartner, 90% of organizations worldwide are predicted to value data as a “critical enterprise asset” and predictive analytics as an “essential competency” in 2022. By identifying the data trends and patterns, predictive analytics help businesses forecast future events and bridge the gap in data sets. One such important statistical technique used in data analytics is linear regression. So, what is linear regression, and how does it work? What are its real-world applications? How is it useful in machine learning?

In this guide, we’ll explore everything you need to know to get started with linear regression analysis. ## What is Linear Regression?

According to AWS, linear regression is a data analysis technique that predicts the value of unknown data by using another related or known data value.

Thus, linear regression mathematically models the relationship between dependent and independent variables as a linear equation. For example, let’s say you have data about your expenditures and income for last year. The linear regression model analyzes this data to determine that your expenditures are half your income. You can further apply this model to predict an unknown future expense by having a known future income.

## How Does Linear Regression Work?

Although at one glance, mastering linear regression analysis might seem like a daunting task. However, it’s not that complex. Let’s do a quick recall. At some point, while studying in school, you must have plotted two data set points one against the other to determine what’s called the ‘line of best fit’. You must have then used this line to predict values missing from the given dataset. In its fundamental form, this is what linear regression is.

Therefore, linear regression uses a linear equation that we can plot on a graph. While there are different linear regression equations (for simple and multiple linear regression), the simple equation (with one input variable) we can plot in the form:

Y= mX+b

Where,

• Y is the dependent variable
• X is the input variable
• m is the regression slope
• b is the Y-axis intercept

## Why is Linear Regression Important?

Linear regression is important for various reasons. Firstly, it has pure statistical implications:

• Predicts future outcomes by identifying missing data values
• Estimates correct data values by identifying the possible errors in a dataset
• Measures the relationship strength between data sets by determining the R square value (which measures the standard deviation between independent and dependent variables)

Moreover, it is used as an established statistical model that applies easily to computing and software analysis to generate predictions. Companies leverage the reliability of linear regression to convert raw data into actionable insights to make informed business decisions. Data scientists use linear regression to perform data analysis, predict future trends, and solve complex problems related to machine learning models and artificial intelligence.

To summarize, the linear regression model is important because it is:

• Easy to interpret
• Accurate
• Has various applications
• More reliable than business instincts

## What is Linear Regression Used for in Real-World Applications

It’s good to have theoretical knowledge of linear regression, but it is also essential to understand how it can be applied to real-world scenarios.

Let’s look at how the concept applies in three key industries:

### Healthcare

Linear regression can be used to predict how patients will react to a new medication. It is commonly applied to determine a metric known as ‘Length of Stay’ (LOS) for patients. By using previous data on the length of stay, illness, diet, and age, the model predicts the future outcome. It exposes the inefficiencies in the healthcare industry and ensures that patients get the care they need by enabling healthcare providers to take steps toward shortening LOS.

### Finance

In the finance industry, linear regression is used for time series analysis. This involves analyzing the data sets spaced at regular intervals (such as stock market data or shifts in the price of gold). Modeling the data will help to predict future values like exchange rates, interest rates, and selling prices. In insurance, linear regression models are also used to predict risks.

### Retail

Linear regression in retail predicts future product sales, stock replenishment requirements, and customer behavior. A linear regression model can help retailers predict expenditures with a high degree of accuracy. The model enables them to meet their marketing goals by tailoring messages and customer experiences to target individual customers with specific products they may be interested in.

## What is Linear Regression in Machine Learning

Linear regression algorithm is used for supervised machine learning. It applies relations to generate predictions and outcomes of an event based on independent variable data points. The relationship is usually a straight line on a graph that best fits the varied data sources as closely as possible.

In machine learning, computer algorithms analyze large data sets and work backward from the data points to calculate the linear regression equation. Firstly, data scientists train and tune the algorithm on labeled datasets and then implement the algorithm to predict unknown values.

## What are the Key Assumptions for Simple Linear Regression?

To simplify machine learning datasets, the linear regression model mathematically transforms or modifies the data points according to the following three assumptions:

### 1. Linear Relationship

There should be a linear relationship between the independent and dependent variables. To determine if a linear relationship exists, data scientists build a scatter plot by randomly plotting the X and Y values to check whether they fall in a straight line. If not, they use non-linear functions such as square root or log to create a linear relationship between the values.

### 2. Residual Independence

A residual is the difference between observed values and predicted values. Data scientists do not want the residual differences to increase with time. Hence, they use the Durbin-Watson test to establish residual independence by using dummy data to replace any data variation.

### 3. Homoscedasticity

Homoscedasticity assumes that the margin of error is constant throughout the dataset. It denotes that residuals have a constant variance or standard deviation from the average of every value of ‘x’. For instance, as money increases, happiness increases. However, if our findings indicate, as money increases, there is a drastic rise in happiness- then what we have is known as heteroscedasticity.

## What is Linear Regression and Logistic Regression Difference?

A simple linear regression estimates the relationship between two quantitative variables. For instance, you can determine how strong the relationship is between two variables (such as rainfall and crop yield) or use it to estimate the value of the dependent variable at a particular value of an independent variable (such as the amount of crop yield at a certain rainfall level).

On the hand, logistic regression measures the probability of an event occurring. The prediction provides a value between 0 and 1, where 0 indicates the event is unlikely to happen, and 1 denotes the maximum chance of occurrence. Some examples are the probability of winning/losing an election or passing/failing a test.

## How to Learn About Linear Regression

While this topic on ‘what is linear regression’ covers the basis, there is so much more to learn about this statistical technique and apply it in predictive analytics! So, enroll in one of Emeritus’ top-notch online data science and analytics courses and get hands-on data science training to gain experience that will help you land a top data scientist role.

By Swet Kamal

Write to us at content@emeritus.org 