Hat Matrix Leverage

Problem

For simple linear regression with an intercept, compute the leverage (hat matrix diagonal) of each observation: h_i = 1/n + (x_i - mean_x)^2 / Sxx, where Sxx = sum((x_j - mean_x)^2).

If Sxx is 0, return 1/n for every point. Empty input returns [].

Hint

Leverage grows with the squared distance of x_i from the mean; all leverages sum to the number of parameters.

Test cases

case 1

in: [[1,2,3,4]]

expected: [0.7,0.3,0.3,0.7]

case 2

in: [[5,5,5]]

expected: [0.3333333333333333,0.3333333333333333,0.3333333333333333]

case 3

in: [[0,1]]

expected: [1,1]

case 4

in: [[7]]

expected: [1]

Starter codePython

def leverage_values(X):
    # Your code here
    pass

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