What is a bias term in linear regression?

In linear regression, the bias term, often referred to as the intercept, is a constant that is added to the linear equation. This constant allows the model to have more flexibility in fitting the data. By including the bias term, the model can adjust vertically on the graph, enabling it to fit datasets that do not necessarily pass through the origin (0,0). This is crucial because real-world data often does not align perfectly along the axes, and having the bias term helps ensure that the model can better approximate the underlying data distribution.

For example, if you were predicting housing prices based on various features (like square footage or number of bedrooms), the inclusion of the bias term means that even if all input features are zero, your model can still predict a baseline price, which could represent the value of a house that has no features at all. This adaptability enhances the fit of the model, especially when addressing cases where the relationship between inputs and outputs is not strictly linear.