Problem

Let

$$f(\beta)=\sum_{i=1}^n\left(y_i-1-\beta x_i+2x_i\right)^2.$$

Suppose that $\sum_{i=1}^n x_i=-5$, $\sum_{i=1}^n y_i=5$, $\sum_{i=1}^n x_i^2=15$, and $\sum_{i=1}^n x_i y_i=10$. Find $\beta$ that corresponds to the minimum of $f$.

(a) $2/3$

(b) $4/3$

(c) $8/3$

(d) $7/3$

(e) None of the above.