Residuals and traps

You will write four functions that judge a straight-line fit: the residuals, the sum of the squared residuals, the coefficient of determination and a test for a point that changes $r$ a lot. The helper fit is already written. It returns the intercept and the slope.

The idea. A residual is $y - \hat{y}$, the vertical miss. The residuals of the least squares line add to zero. The coefficient of determination is $r^2 = 1 - \dfrac{\text{sum of squared residuals}}{S_{yy}}$. A point is influential if removing it changes $r$ a lot.

Your tasks.

1. Finish residuals(x, y).
2. Finish sum_squares(x, y), the sum of the squared residuals.
3. Finish r_squared(x, y).
4. Finish influential(x, y, i). Return True when removing point number i changes $r$ by more than $0.5$.