# Is there a connection between the bias term in a linear regression model and the bias that can lead to under-fitting?

Here is a linear regression model

$$y = mx + b,$$

where $$b$$ is known as $$y$$-intercept, but also known as the bias [1], $$m$$ is the slope, and $$x$$ is the feature vector.

As I understood, in machine learning, there is also the bias that can cause the model to underfit.

So, is there a connection between the bias term $$b$$ in a linear regression model and the bias that can lead to under-fitting in machine learning?

1. A (learnable) parameter of a model, such as a linear regression model, which allows you to learn a shifted function. For example, in the case of a linear regression model $$y = f(x) = mx + b$$, the bias $$b$$ allows you to shift the straight-line up an down: without the bias, you would only be able to control the slope $$m$$ of the straight-line. Similarly, in a neural network, you can have a neuron that performs a linear combination of the inputs, then it uses a bias term to shift the straight-line, and you could also use the bias after having applied the activation function, but this will have a different effect.