Please follow the instructions and implement codes

The least squares regression coefficients can be calculated via the closed form solution:

=(XTX)1XTY=(XTX)1XTY

First try it out with using np.dot (anywhere there is a matrix multiplication) and np.inv (anywhere there is a matrix inversion. (as a note, matrix transposition is accomplished with .T)

Next, compare using np.linalg.lstsq -- numpy's built in least squares regression (that is much more stable than using the matrix inversion f

#Least Squares Estimation Goes Here

#TODO replace the np.zeros() with the correct code

def calculate_weights_with_linear_algebra(X: np.array, Y: np.array) -> np.array: return None

def calculate_weights_with_library(X: np.array, Y: np.array) -> np.array: return None

B_raw = calculate_weights_with_linear_algebra(X,Y) B_lstsq = calculate_weights_with_library(X,Y)

#This should be small, mostly in the 1e-13 to 1e-14 range print(B_raw-B_lstsq)