Introduction

Imagine you're trying to predict house prices. You know that things like square footage, number of bedrooms, and location matter. Linear regression is like finding the best straight line to represent this relationship.

Linear regression is a statistical method used to model the relationship between a dependent variable (the one you want to predict) and one or more independent variables (the predictors). It assumes a linear relationship between these variables, meaning the data points tend to cluster around a straight line.

How it works?

Consider You have a labeled tabular data in which you have one dependent feature(the one you want to predict) and the other one is independent feature

Lets Understand it with an example
Imagine you have an ice-cream shop just imagine, our Goal is Machine Learning :) now you want to predict sales of your ice-cream shop on the basis of temperature. See clearly we have got our two features The Dependent one and The Independent one. Yes you got it right The Sales is dependent on Temperature.
Lets see how our tabular data look will like:
 


Now lets consider these sales are our data points with respect to the temperature and if we plot them on a XY Plane it will look something like this




Goal of Linear Regression

The goal of linear regression is to find the best-fitting line through the data points. This line represents the relationship between the variables. And then we will predict our new data point with the help of that line and yes, that's it we successfully predict our new data point which is our new sales on that particular temperature




The equation for a simple Linear Regression (with one independent variable) is:
 
y=mx+b

  • y is the dependent variable
  • m is the slope of the line
  • x is the independent variable
  • b is the y-intercept

    • For multiple linear regression (with multiple independent variables), the equation becomes:

    y = b0 + b1x1 + b2x2 + ... + bn*xn

    Where:

    • y is the dependent variable
    • b0 is the intercept
    • b1, b2, ..., bn are the coefficients for each independent variable
    • x1, x2, ..., xn are the independent variables

    Key Concepts

    • Residuals: The difference between the actual value and the predicted value.
    • Mean Squared Error (MSE): A measure of the average squared difference between the predicted and actual values.
    • R-squared: A statistical measure that represents the proportion of variance in the dependent variable that is explained by the independent variable(s).

    When to use

    • Predicting a continuous numerical value.
    • Understanding the relationship between variables.
    • Identifying important predictors.

    Limitations

    • Assumes a Linear relationship between variables
    • Sensitive to outliers
    • Might not capture complex relation


    Conclusion

     Linear regression is a powerful tool for understanding and predicting relationships between variables. While it has limitations, it remains a fundamental technique in data science and statistics.