Question

Consider the following data points
(1, 4)
(2, 9)
(3, 6)
(4, 10)
Use partial derivatives to obtain the formula for the best least-squares fit to the data points.

Answer 1

It will look like a square

Answer 2

i got y(x)=-30.5x+99.5 which is wrong..

Answer 3

so far i got
\[L(x)=\frac{5}{3}(x-1)(x-2)(x-3)- \]
\[3(x-1)(x-2)(x-4)-\frac{9}{2}(x-1)(x-3)(x-4)-\frac{2}{3}(x-2)(x-3)(x-4) \]

Answer 4

i didn't feel like write it in standard form
http://www.wolframalpha.com/input/?i=5%2F3%28x-1%29%28x-2%29%28x-3%29-3%28x-1%29%28x-2%29%28x-4%29-9%2F2%28x-1%29%28x-3%29%28x-4%29-2%2F3%28x-2%29%28x-3%29%28x-4%29

Answer 5

this is my work
i hope you can read some it lol

Answer 6

i did it with Lagrange polynomials