Consider the following set of data:

x $0\mathrm{.}10\mathrm{.}20\mathrm{.}40\mathrm{.}60\mathrm{.}91\mathrm{.}31\mathrm{.}51\mathrm{.}71\mathrm{.}8$

y $0\mathrm{.}751\mathrm{.}251\mathrm{.}451\mathrm{.}250\mathrm{.}850\mathrm{.}550\mathrm{.}350\mathrm{.}280\mathrm{.}18$

Perform a least squares regression to fit the data to the following curve:

y $=\backslash$alpha $1$xe$^(\backslash$alpha $2$x$)$

$.$ Be sure to show the following steps on paper:

$$ linearization of y $=\backslash$alpha $1$xe$^(\backslash$alpha $2$x$)$ with respect to the parameters $(\backslash$alpha $1,\backslash$alpha $2)$

$$ Define the sum of squared errors Sr

$$ Differentiation of Sr with respect to each of the free parameters

$$ Definition of the normal equations

$$ your estimate for $\backslash$alpha $1,\backslash$alpha $2$

Once these steps have been shown, feel free to code the normal equations in

matrix vector form and solve with Python. Be sure to show snapshots of any

code as well as the estimates for the parameters $\backslash$alpha $1,\backslash$alpha $2.$ Finally, generate a plot

of the curve fit compared to the given data