Fitting a Straight Line into Empirical Data (Regression). In a 10-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 1 2 3 4 5 6 7 8 9 10 Words per minute, y 5 9 15 19 21 24 26 30 31 35 Determine the coefficients a and b in the straight-line relationship, yn = ax +

b, that best fit the given data. (Hint: Minimize the sum of the absolute value of the deviations between theoretical yn and empirical y. Min •w• is equivalent to min z subject to z Ú w and z Ú -w, z Ú 0. Alternatively, min •w• is equivalent to min 1z+ + z-2 subject to w = z+ - z- with z+, z- Ú 0.)