1. The problem statement, all variables and given/known data We have the following x, y values x ||| y 1.0 -0.15 1.5 0.24 2.0 0.68 2.5 1.04 3.0 1.21 3.5 1.15 4.0 0.86 4.5 0.41 5.0 -0.08 How can you find the equation [tex]y(x) = ax^2 + bx + c[/tex] by least squares? 3. The attempt at a solution I know how to calculate the equation for a line by solving Ax = b taking transposes of A at the both sides [tex]A^TAx = A^Tb[/tex] and then solving for x. My second attempt I made a 9 x 3 matrix for A where the first two columns are ones, 3 x 1 for x and 9 x 1 for b. However, I get a singular matrix for [tex]A^TA.[/tex] Apparently, my method is not right. I could make 3 equations such as y(0), y(1) and y(2) and solve for a, b and c. However, I see that the method is not least squares and also rather inaccurate, since not all points are considered.