# What is the use of additional column of 1s in normal equation?

Currently I am going through Normal Equation in Machine Learning.

$$\hat\theta = (X^T \cdot X)^{-1} \cdot X^T \cdot y$$

But when I see how they use this equation, I found they always add an additional column of 1s in the starting of matrix X before transposing.

I don't understand why. What's the logic behind this?

The places where I found such things

1) Coursera - Theory

2) Implementation

Now let’s compute using the Normal Equation. We will use the inv() function from NumPy’s Linear Algebra module (np.linalg) to compute the inverse of a matrix, and the dot() method for matrix multiplication: X_b = np.c_[ np.ones(( 100, 1)), X] # add x0 = 1 to each instance

Géron, Aurélien. Hands-On Machine Learning with Scikit-Learn and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems (p. 111). O'Reilly Media. Kindle Edition.

• They represent intercept term, also called bias. – Vaalizaadeh Feb 18 '18 at 7:30