Linear regression is a popular method in machine learning that helps to establish a relationship between two variables. In this technique, we aim to predict a continuous numerical value or a dependent variable (y) based on one or more independent variables (x). The process of regression helps in identifying the strength of the relationship between variables.

Linear regression is a simple but powerful technique that can be applied to several problems in different fields, including finance, economics, social sciences, and biology. In machine learning, linear regression is one of the most basic and essential tools for the prediction of outcomes.

The basic idea behind linear regression is to find a line that best fits the data. The line or equation will describe the relationship between the independent variable and the dependent variable. When we plot the dependent and independent variables on a graph, we can see the trend of the data points. The best line will be the one that minimizes the distance between the actual data points and the line.

The line equation takes the form y = mx + c. We estimate the slope (m) and the intercept (c) of the line using a technique called least-squares fitting. The slope (m) represents the change in the dependent variable for each unit change in the independent variable, and the intercept represents the value of the dependent variable when the independent variable is zero.

In machine learning, we use linear regression to find a mathematical function that will describe the relationship between the input features and the output value. Specifically, we aim to find a set of weights, which when multiplied with each feature, will give us the predicted output value.

Linear regression can be further classified into two types:

1. Simple linear regression: When we have a single input feature, we use simple linear regression. The linear function takes the form y = mx + c, where y is the dependent variable, x is the independent variable, m is the slope, and c is the intercept.

2. Multiple linear regression: When we have two or more input features, we use multiple linear regression. The linear function takes the form y = w0 + w1*x1 + w2*x2 + … + wn*xn, where wn are the weights learned during training, and x1, x2, …, xn are the input features.

In summary, linear regression is a powerful and straightforward tool in machine learning for predicting continuous numerical values. Whether you have one or several input features, linear regression is a great place to start for understanding the relationship between variables.