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Linear Regression – Types and Applications Explained

Machine learning has become one of the most sought-after branches of AI that focuses on algorithms and data to imitate the process of how a human learns and improves accuracy. In ML or machine learning, the most straightforward algorithm is linear regression.

It is a straightforward method for predictive analysis. If a student wants to enroll in a Machine learning and Artificial Intelligence course, they need to learn what linear regression is. Mentioned below is a comprehensive analysis of linear regression.

## What Is Linear Regression?

Regression is the supervised learning methodology that enables the process of discovering correlations among variables. Regression problems arise when an output variable is a continuous or real value. Linear regression showcases the relationship between constant variables. It shows a linear relationship between the X-axis or independent variables and Y-axis or dependent variables.

Suppose there's one input variable, i.e., X; it will be simple linear regression. If more than one input variable is present, multiple linear regression will occur.

Want to learn about bagging and boosting in ML? What is Bagging vs. Boosting in Machine Learning? Click on the link to learn further.

## Understanding Linear Regression

To understand everything about linear regression, you first need to get an insight into its importance in ML. In short, it is one of the most important algorithms belonging to supervised ML.

What it does is try applying relations that predict an outcome of the event depending on the independent variables' data points. This relation happens to be a straight line that fits various data points. Its output is continuous, so it is in a numerical value.

## How Linear Regression Works

To understand how linear regression works, you need to know its mathematical representation. In mathematics, it can be expressed in the following equation:

```y= β0+ β 1x+ ε, where:
Y is the dependent variable
X is the Independent Variable
β 0 is the intercept of that line
β1 is the linear regression coefficient (or the line's slope)
ε is the random error
```

Note that the linear regression algorithm shows the linear relationship between y and y (a dependent and one or more independent variables). So, that means it finds the value of the dependent variable changing as per the change in the value of an independent variable. As a matter of fact, the relationship between dependent and independent variables is a straight line with a slope.

Discover everything about Regression Testing - Meaning, Types and Tools by clicking on the link.

## Why Is Linear Regression Important?

Linear regression is important only due to the fact that it offers a scientific calculation that identifies and predicts future outcomes. Its ability to find predictions and assess them can offer rewarding benefits to individuals and businesses. Linear regression can perform greatly for linearly separable data.

In addition, it is seamless to implement and effective to train. Besides, it also handles overfitting using dimensionally reduction techniques, cross-validation, and regularisation. The last advantage of linear regression is the extrapolation beyond its specific data set.

## Types of Linear Regression and Their Applications

If you want to learn about the various types of linear regression and applications, you may note down the following details:

### 1. Simple Linear Regression

There are majorly two types of linear regression. The first one is the simple linear regression. If one independent variable is used for predicting the numerical value's dependent variable, it is known as simple linear regression.

Simple linear regression shows the relationship between a dependent variable and an independent variable through a straight line.

#### How Simple Linear Regression Works

A statistical method used for establishing a relationship between two variables via a straight line, simple linear regression has several applications. But first, let's know how it works. Simple linear regression helps model a relationship between two continuous variables. The prime goal is to anticipate a value of the output variable depending on the input's value.

Simple linear regression is implemented in the following ways in the practical world. If you wish to learn about them, please get a brief insight into the best linear regression examples:

• Used for demonstrating the marks of students
• It can also assess the number of hours someone works
• It also excellently predicts crop yields based on the rainfall

Lastly, it can help predict the salary of any individual based on their years of experience

#### How to Implement Simple Linear Regression?

SLR is implemented in the following ways:

• First, the data is loaded
• Then, it is explored
• After this, data slicing occurs
• Training and splitting data
• Generating model
• Lastly, evaluating the accuracy

### 2. Multiple Linear Regression

Among the two types of linear regression, multiple linear regression is the second one. If there's more than one independent variable, the overall governing linear equation takes another form. Here, the equation is y= c+m1x1+m2x..

It is multiple linear regression, or MLR, where it demonstrates a mathematical relationship among various variables. MLR examines how an independent variable gets correlated to a dependent one.

#### How It Differs from SLR or Simple Linear Regression

Multiple linear regression evaluates the relative impacts of independent or explanatory variables on dependent ones. At the same time, it also holds other variables in the model constant. It is different from SLR:

SLR involves just one x and y variable, while MLR involves more than one x and one y variable.

Here's enlisting the most common real-world linear regression examples.

• Measures the temperature, fertilizer impacts, and rainfall
• Anticipates values for variables under situations like police confidence between sexes and controlling the influence of ethnicity and other factors

#### How to Implement Multiple Linear Regression?

Here's how MLR is implemented:

• Libraries get implemented
• Import Dataset
• Data Pre-Processing occurs
• Splitting the data into testing and training set
• Model Training
• Model Evaluating

### 3. Polynomial Regression

This is a technique used for anticipating the outcome. Let's understand how it works in the following point:

#### How Polynomial Regression Works:

Polynomial regression is the relationship between independent as well as dependent variables. Here, the dependent variable and independent variable are interconnected with the nth degree.

The polynomial regression model happens to be a machine learning model that captures nonlinear relationships between variables by fitting the nonlinear regression line. It may not be possible with the SLR.

#### How to Implement Polynomial Regression?

Here's a brief understanding of the implementation of polynomial regression:

• Data Pre-processing takes place in the initial phase
• After this, a Linear Regression model is built & fit to a dataset
• Then, a Polynomial Regression model is built & fit into the databaseVisualising results for Linear Regression as well as Polynomial Regression model.
• Lastly, predicting the output

### 4 . Logistic Regression

Logistic regression is a statistical technique employed to understand the association between a binary dependent variable and one or more independent variables. Unlike SLR, which focuses on predicting a continuous outcome, logistic regression is tailored for predicting the probability of an event occurring or not.

How Logistic Regression Works?

Much like SLR, logistic regression aims to model the relationship between variables. However, the key distinction lies in the nature of the dependent variable, which is binary in logistic regression. This binary outcome could be represented as 0 or 1, yes or no, true or false, making logistic regression particularly useful in scenarios where the outcome is categorical.

The logistic regression process involves utilising the logistic function to convert a linear combination of independent variables into a probability score. The logistic function, also known as the sigmoid function, constrains the output to a range between 0 and 1. This probability score is then used to classify observations into different categories.

### 5. Ordinal Regression

Ordinal regression is a statistical approach designed to analyse and understand the relationship between an ordinal dependent variable and one or more independent variables. Unlike SLR, which focuses on predicting continuous outcomes, ordinal regression tackles scenarios where the dependent variable is ordered or ranked.

How Ordinal Regression Works?

Similar to SLR, ordinal regression aims to model the relationship between variables, but it is tailored for situations where the outcome variable has inherent order or hierarchy. This hierarchy could include categories like low, medium, high, or any other ordered scale.

The essence of ordinal regression lies in predicting the likelihood of an observation falling into a particular category or order. It utilises cumulative probability functions to estimate the probabilities associated with each category, considering the order and the distance between categories.

## Assumptions of Linear Regression

Linear regression is the analysis assessing whether one (or more) predictor variables elucidate dependent (criterion) variables. A regression comprises five assumptions, including the following:

• A linear relationship between variables (assuming that a linear relationship is there between independent and dependent  variables)
• Data Normality  (where the model assumes the data to follow a regular distribution, where most data falls within a bell-shaped curve's central region on the graph)
• Data Homogeneity (a regression model assuming all variables to have the same characteristics, for example, the standard of the error to be the same)

### Applications of Linear Regression

Enlisted below are the applications of linear regression:

• Market analysis by using some marketing strategies and maximising sales
• Financial study through linear models for evaluating an establishment's operational performance
• Sports analysis by predicting game attendance depending on the team's status as well as market size
• Predicts the impact of water and air pollution on the environment
• Recognizes high-risk patients and improves healthy lifestyles

### Difference between Overfitting and Underfitting

Let’s explore the key differences between the types of Liner regression on detail:

Differences Based on Parameters Overfitting Underfitting
Definition It is a common pitfall in deep learning where the model fits training data, memorises data patterns and noise fluctuations. Such models cannot generalise or perform greatly (in case of unseen data, so it defeats the purpose of the model. The main difference between underfitting and overfitting is that the former, fails to create a mapping between an input and target variable. Here, the model performs greatly in a training set but fails to generalise learning to a testing set.

How to Avoid

More data training

Data augmentation

Cross-validation

Data simplification

Regularisation and more

Decrease regularisation

Increase trainin duration

Removing noise from data

## Conclusion

This post has compiled everything about linear regression in detail starting from its meaning, types, and applications.

Author Bio: Hero Vired offers digital certification courses and courses in Machine Learning, Artificial Intelligence, Data Science, and more.

## FAQ's

There are three prime metrics for model evaluation in regression, and they are mentioned in the following:
• R Square or Adjusted R Square
• Mean Square Error(MSE) or Root Mean Square Error(RMSE)
• Mean Absolute Error(MAE)
Linear regression is the data analysis method used for predicting the value of data using known or related data values. It models a dependent variable and an independent variable as the linear equation.
The major types of linear regression are simple linear regression and multiple linear regression.
The purpose of regression analysis is twofold. Firstly, it is utilised to predict the value of the dependent variable for individuals when information about the explanatory variables is known. Secondly, it is employed to estimate the impact of specific explanatory variables on the dependent variable, providing insights into their relationship and contribution to the overall analysis.
The objective of the SLR algorithm is to determine the best-fitting line through given data points. This is achieved by identifying the line that minimises the sum of the squared differences between each data point and the line, providing an optimal representation of the linear relationship between the variables.
1. LR relies on four key assumptions:

• Linearity: The relationship between the independent variable (X) and the mean of the dependent variable (Y) is linear.
• Homoscedasticity: The variance of residuals (differences between observed and predicted values) is consistent across all levels of the independent variable.
• Independence: Observations are independent of each other.
• Normality: For any fixed value of X, the dependent variable Y is normally distributed.
These assumptions are fundamental for the accuracy and reliability of the LR model.
A basic example involves predicting the value of a dependent variable based on an independent variable. For instance, one can use it to forecast temperature changes, where the temperature increases as the sun rises and decreases during sunset. This demonstrates a simple relationship between independent and dependent variables, making it a straightforward illustration in action.
It finds applications across diverse fields in both business and academic research. Its versatility is evident in its use in biological, behavioural, environmental, and social sciences, as well as in business contexts. LR models serve as a reliable and scientific method for predicting future outcomes, making them valuable tools for decision-making and analysis in a wide range of disciplines.

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