A worker would like to know how wage responds to grades. The assumption
is that wage is linear in the grade (w = q1 + q2s).
(1) The worker has two observations: one person with wage w1 and grade
s1, another with different w2 and different s2. Find q1 and q2.
(2) A third observation is added: w3 together with s3. Assume w3 is different from w1,w2 and s3 from s1,s2. The worker fits a line to the three observations by minimizing the sum of the squared vertical distances between the line and the data points. Write the minimization problem and solve for q1 and q2. The vertical distance between a line y = ax + b and a point (x0, y0) is |y0 - ax0 - b|. (3) The worker assumes that q2 ≥ 0. Solve the previous minimization problem again, with this constraint added.