Linear Regression is a method for modelling a relationship between a dependent variable and independent variables. These models can be fit with numerous approaches. The most common is least squares, where we minimise the mean square error between the predicted values y^=Xβ^ and actual values y: (y−Xβ)2
Linear Regression is a supervised machine learning algorithm where the predicted output is continuous and has a constant slope. It’s used to predict values within a continuous range, (e.g. sales, price) rather than trying to classify them into categories (e.g. cat, dog).
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Linear regression is defined as the relationship between a dependent variable (Y) and an independent variable (X). It employs a regression line, also known as a best-fit line. The linear connection is defined as Y = c+m*X + e, where ‘c’ denotes the intercept, ‘m’ denotes the slope of the line, and ‘e’ is the error term.
Linear regression is divided into two types:
similar linear regression where we have one dependent variable and one independent variable.
multiple linear regression models where we have one dependent variable and many independent variables.
DIFFERENCE TYPES OF CORRELATIONS
When we fit the linear regression model we can see three types of relationships exist: positive correlation ,negative correlation, zero correlation or No correlation from above graphs we see that in positive correlation the slope is in increasing direction whereas in negative correlation the slope is in decreasing direction and in No correlation it is constant.
Gradient Descent:
Gradient descent is used to minimise the MSE by calculating the gradient of the cost function.A regression model uses gradient descent to update the coefficients of the line by reducing the cost function.It is done by a random selection of values of coefficient and then iteratively updating the values to reach the minimum cost function.
Applications Of Linear Regression:
Linear regression is a powerful statistical technique. Linear regression can also be used to analyse the marketing effectiveness, pricing and promotions on sales of a product.
Linear Regression can be also used to assess risk in financial services or insurance domain.
In the credit card industry, a financial company may be interested in minimising the risk portfolio and wants to understand the top five factors that cause a customer to default.
Implementation Of Linear Regression
From Scratch using Python programming
Using predefined libraries and package like sklearn
Linear Regression from Scratch Using Python:
Importing the required libraries
Here I am using the sample dataset which consists of 2 features and one dependent variable And I am taking the feature_1 and target columns for training the model.
Splitting the dataset into x and y labels
For linear regression we use different type of metrics like r2_score,mean_squared_error for for calculating the covariance we are using (m = cov(x, y) / var(x)
, b = y - m*x)
Building Linear regression: here we are building the linear regression model and splitting the dataset ,predicting the values and finding the r2-score and MSE score .
Here we are plotting the regplot for x and y
output :
And here finally we are plotting the predicted labels and representing the predicted line in graph.
Output :
Linear Regression using Sklearn library:
Scikit-learn (Sklearn) is the most useful and robust library for machine learning in Python. It provides a selection of efficient tools for machine learning and statistical modeling including classification, regression, clustering and dimensionality reduction via a consistent interface in Python.’
Here we are using the sklearn library for linear regression
Using : from sklearn.linear_model import LinearRegression
Here also we are using the same dataset as above
Additional libraries:
Splitting the dataset:
Model building;
Prediction of Test and Training set result:
Plotting regression graphs for both the train dataset and test datasets:
Output :
Output :
Common packages, Methods, tools, Libraries used
LinearRegression methods of sklearn.linear_model
r2_score, mean_squared_error
pandas, numpy, matplotlib, seaborn
train_test_split
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