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# Linear Regression Algorithm. Explained...

Shashank Shanu

3 years ago

• A step by step explanation of the Linear Regression Algorithm.
• What is Regression?
• Types of Regressions
• What is a Linear Regression?
1. Simple Linear Regression/ Univariate Linear Regression
1. The mathematics involved
2. How do we know this is the best fit line?

## A step by step explanation of the Linear Regression Algorithm

Hello Folks,
Hope you are well and staying safe at your place. As we all know how this COVID-19 pandemic came and doesn't want to go from our life.
But as the whole world is fighting to get rid of this pandemic. I thought why can't I share some things which I know so that many people may get benefits from it.
Before directly going deep into the Linear regression algorithm.
Let us first understand

## What is Regression?

Regression is a statistical technique that shows an algebraic relationship between two or more variables.
Based on this algebric relationship (rather than a function), one can estimate the value of a variable, given the values of the other variables.
Usually, correlation is used to check whether there is any relationship between the two variables. If any relationship found, regression is used to find the degree of relationships that can be then used for prediction.
Some of the examples are:
• Predict rainfall in cm for month
• Predict stock price for next day
Now as you got an idea about what is regression? Let’s move forward and see what are the types of regressions?

## Types of Regressions

• Linear regression
• Logistic regression
• Polynomial regression
• Stepwise regression
• Ridge regression
• Lasso regression
• ElasticNet regression
In this article I will explain you about Linear Regression and later I will try to take you through the other types of regressions.

## What is a Linear Regression?

Linear Regression is one of the most fundamental algorithms in the Machine Learning world which comes under supervised learning. Basically it performs a regression task. Regression models predict a dependent (target) value based on independent variables. It is mostly used for finding out the relationship between variables and forecasting. Different regression models differ based on – the kind of relationship between the dependent and independent variables, they are considering and the number of independent variables being used.
Linear regression performs the task to predict a dependent variable value (y) based on a given independent variable (x). So, this regression technique finds out a linear relationship between x (input) and y (output). Hence, the name is Linear Regression.
In the figure above, X (input) is the work experience and Y (output) is the salary of a person. The regression line is the best fit line for our model.
Linear Regression may further divided into
1.  Simple Linear Regression/ Univariate Linear regression
2.   Multivariate Linear Regression

### Simple Linear Regression/ Univariate Linear Regression

When we try to find out a relationship between a dependent variable (Y) and one independent (X) then it is known as Simple Linear Regression/ Univariate Linear regression.
The mathematical equation can be given as:
Y = β0 + β1*x
Where
• Y is the response or the target variable
• x is the independent feature
• β1 is the coefficient of x
• β0 is the intercept
β0 and β1 are the model coefficients (or weights). To create a model, we must "learn" the values of these coefficients. And once we have the value of these coefficients, we can use the model to predict the target variable such as Sales!
NOTE: The main aim of the regression is to obtain a line that best fits the data. The best fit line is the one for which total prediction error (all data points) are as small as possible. Error is the distance between the points to the regression line.
Let us consider Real-time example
Let’s suppose we have a dataset which contains information about the relationship between ‘a number of hours studied’ and ‘marks obtained’. Many students have been observed and their hours of study and grade are recorded. This will be our training data. The goal is to design a model that can predict marks if given the number of hours studied. Using the training data, a regression line is obtained which will give the minimum error. This linear equation is then used for any new data. That is, if we give the number of hours studied by a student as an input, our model should predict their mark with minimum error.

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