Solving a simple Linear Regression problem using CVX and Matlab

Caution: Contains over-(simplification, generalization, and some other *tions)

Homer is a hawker who sells batman toys. Kids love those very much and his business is on the rise. He noticed that for the past five days, these are his costs and profits:

Items Sold	Profit
100	960
80	760
70	660
150	1460
90	860

Now, a competitor, Ned, has stolen these data and wants to know a little more about his daily operating expense and per item price. Ned is a very good statistician and feels that these data should form a nice regression problem expressed in the following equation:

y = b0 + b1*x

Where 'y' is the value of profit, 'b0' is the fixed cost that Homer incurs everyday and 'b1' is the per price item and 'x' is the number of items Homer sells everyday.

Ned recently bought a license of Matlab and downloaded cvx, a nice modelling tool and thought to give it a try to find out Homer's secrets.

He writes the following matlab code:

b = [960 760 660 1460 860]; % profit vector
x = [100 80 70 150 90]; % item sold each day

cvx_begin
    variables b1 b0 % b1 = per item price, b0 = fixed cost per day
    minimize(norm(((b1*x) + b0) - b )) % minimizing the estimated and actual values
cvx_end

And yes, he finds that per day cost is 40 and per item price is 10. (For Algebraist: ya, I know)