Given the following data points

$x_i=[0,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}8,1]$

$f_i=[1\mathrm{.}05,0\mathrm{.}8,0\mathrm{.}72,0\mathrm{.}84,1\mathrm{.}2,1\mathrm{.}95]$

Using least squares method, fit into a polynomial of order $n=3.$ write the equation of the fitted data $f(x)$ and find $f(0\mathrm{.}5).$