By using the method of least squares, find the best line through the points:
    ,   ,   .  

Step 1. The general equation of a line is . Plugging the data points into this formula gives a matrix equation .

Step 2. The matrix equation has no solution, so instead we use the normal equation


Step 3. Solving the normal equation gives the answer

which corresponds to the formula

Analysis. Compute the predicted values: .

Compute the error vector: .

Compute the total error: .

You can earn partial credit on this problem.