why gradient descent when we can solve linear regression analytically

When you use the normal equations for solving the cost function analytically you have to compute:

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Where X is your matrix of input observations and y your output vector. The problem with this operation is the time complexity of calculating the inverse of a nxn matrix which is O(n^3) and as n increases it can take a very long time to finish.

When n is low (n < 1000 or n < 10000) you can think of normal equations as the better option for calculation theta, however for greater values Gradient Descent is much more faster, so the only reason is the time 🙂

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