If you want to solve this problem by using only linear regression then you need to use normal equations for solving the cost function analytically.

**Equation:**

In the above equation, X is your matrix of input observations and y is your output vector. The problem with this operation is the time complexity of calculating the inverse of an nxn matrix which is O(n^3) and as n increases. This process is **computationally expensive and time-consuming. **

If you use **Gradient Descent**, then it would be a more efficient way to work on a large dataset. That's why we use **optimization algorithms for faster and accurate computation.**

I hope this solution will clear your doubts.