Given x $=[1,2,3,4]$ and y $=[6,5,7,10],$ please find a line of best fit that satisfies y $=$ B$1+$ B$2$x$.$ Your task is to solve the values of B$1$ and B$2$ using the least squares approach and applying the partial derivatives.

Please use Python but do not use Sci$-$kit learn, Scipy, etc libraries where you can solve this in a black box approach. Your task here will be to implement this yourself in Python. You may use Numpy $($but not any solver functions in Numpy$)$ and Sympy libraries. If you would like to use another library please ask first.

Submit your code in a Google Colab notebook.