# The Gradients of Linear Regression cost function

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The cost function for linear regression is:

**J(theta) = (1/2m) * (X * theta — y)^T * (X * theta — y)**

where **X** is the m by (n+1) design matrix, **theta** is the (n+1) by 1 parameter vector, **y** is the m by 1 target vector, and **^T** denotes the transpose operator.

To calculate the gradient of **J(theta)**, we need to take the derivative of **J(theta)** with respect to each element of theta. This can be done using vector multiplication as follows: