3. You're given the following six data points:
(0, 2), (1, −1), (2, 2), (3, 3), (4, −1), (5, 5).
(a) Find the least squares estimates for the regression line $l(x) = \alpha + \beta x$.
(b) Compute the sum of squares of the residuals when approximating the data set by
$l$.
(c) Consider the polynomial
$p(x) = \frac{13}{120}x^5 - \frac{7}{8}x^4 + \frac{29}{24}x^3 + \frac{31}{8}x^2 - \frac{439}{60}x + 2$.
This polynomial can also be used to model the six data points. Compute the sum
of squares of the residuals when approximating the data set by $p$ and explain what
it means.
(d) Suppose we want to estimate the value of Y if X = 6. Compute $p(6)$ and $l(6)$;
what do you notice? Are they in agreement?
(e) Graph $p$, $l$, and the data on a common set of axes.
