For the data points in Exercise 5.5.9, determine the plane z = + x + y that fits the data in the least squares

For the data points in Exercise 5.5.9, determine the plane z = α + βx + γy that fits the data in the least squares sense when the errors are weighted according to the reciprocal of the distance of the point (x_i, y_i, z_i) from the origin.

Data From Exercise 5.5.9

For the data points

(a) Determine the best plane z = a + bx + cy that best fits the data in the least squares sense; 

(b) How would you answer the question in part (a) if the plane were constrained to go through the point x = 2, y = 2, z = 0?

8 Y N 1 1 3 1 2 6 2 1 11 NIN 2 2 -2 3 32 0 34 3 4 3