Given the following data:

$\backslash$table$[[x,$Y$],[0,3],[1,2],[2,3],[3,6],[4,11],[5,18]]$

a$)$ Fit a linear least square fit, $y=a0+a1**x$ Determine the values of $a0$ and a$110$ points

b$)$ What is the correlation coefficient? Checking the correlation coefficient, comment how good the linear fit is $(5$ points$)$

c$)$ Now fit a second order polynomial $y=a0+a1**x+a2**x^2$

Set up the equations for $a0,a1$ and $a2$ as unknowns $($no need to solve for $a0,$ a$1$ and $a2,$ but you need to find out all the equations computing the coefficients.

$10$

points