Regress y on x with an intercept and return (alpha, beta, r_squared), where r_squared = 1 - SS_res / SS_tot.

Input

x = [1. 2. 3. 4.]
y = [2.1 3.9 6.2 7.8]

Output

(0.1500000000000017, 1.9399999999999993, 0.9956613756613757)