Least Squares Through the Origin

Problem

Fit the model y = k*x through the origin to paired data by least squares, where

k = (x . y) / (x . x)

Return the predicted values [k*x[0], k*x[1], ...]. If x is the zero vector, return zeros.

Hint

The slope estimate is the projection of y onto the direction x.

case 1

in: [[1,2],[2,4]]

expected: [2,4]

case 2

in: [[1,2,3],[1,2,3]]

expected: [1,2,3]

case 3

in: [[1,1],[1,2]]

expected: [1.5,1.5]

case 4

in: [[0,0],[1,2]]

expected: [0,0]

Starter codePython

def least_squares_1d(x, y):
    # Your code here
    pass

4 test cases · run your code against them in the editor