Thread: Least Squares problem

Hey!

I have been thinking, but don't get to solve this Least Squares adjust:



Adjust the data below, using least squares, using:
a) First degree function
b) A parabola, with ax² + bx + c

What wrong with just using the definition? If x= 1 then that polynomial gives a+ b+ c and you are told that the correct value is 0.5. The error is a+ b+ c- .5 and the squared error is (a+ b+ c- .5)^2. If x= 2, the polynomial gives 4a+ 2b+ c and your are told that the correct value is .6. The error is 4a+ 2b+ c- .6 and the squared error is (4a+ 2b+ c- .6)^2. Do the same for the other 6 values and add to get the "sum of squares". That will be a function of a, b, and c and you set the partial derivatives with respect to a, b, and c to 0 to give three equations to solve for the values of a, b and c that minimize the sum of squares.