7. Filling a Straight Line into Empirical Data (Regression). In a lO-week typing class for beginners, the average speed per student (in words per minute) as a function of the number of weeks in class is given in the following table.

Week,x Words per minute, y 1

5 2

9 3

15 4

19 5

21 6

24 7

26 8

30 9

31 10 35 Determine the coefficients a and b in the straight-line relationship, y = ax +

b, that best fit the given data. (Hint: Minimize the sum of the absolute value of the deviations between theoretical yand empirical y. Min Ixl is equivalent to min z subject to z :s x and z ~ -x.)