Sum of squares

When the data contains the observations $(x_1,y_1),(x_2,y_2),\dots,(x_n,y_n)$ and the line $y=ax+b$ is fitted to the data, the error can be computed with the sum of squares formula $$\sum_{i=1}^{n}(y_i-(ax_i+b))^2.$$ For example, when the data is $(1,1),(3,2),(5,3)$ and the line is $y=x-1$ (i.e., $a=1$ and $b=-1$), the error is $$(1-(1-1))^2+(2-(3-1))^2+(3-(5-1))^2=2.$$ Implement a class SquareSum with the methods

• add(x, y): add an observation to the data
• calc(a, b): return the sum of squares error for the given line parameters

The time complexity of both methods should be $O(1)$.

In a file squaresum.py, implement a class SquareSum according to the following template:

class SquareSum:
    def __init__(self):
        # TODO

    def add(self, x, y):
        # TODO

    def calc(self, a, b):
        # TODO

if __name__ == "__main__":
    s = SquareSum()
    s.add(1, 1)
    s.add(3, 2)
    s.add(5, 3)
    print(s.calc(1, 0)) # 5
    print(s.calc(1, -1)) # 2
    print(s.calc(0.5, 0.5)) # 0
    s.add(4, 2)
    print(s.calc(0.5, 0.5)) # 0.25