$($It is recommended that you spend no longer than $40$ minutes on this question, including time to upload any file attachments.$)$ Following program uses function linfit to find the line of best fit equation for the provided set of X$-$sorted X & Y data. Develop function linfit so that it receives the X & Y data set and return the coefficients $($slope and $y-$intercept$)$ of the line of best$-$fit equation. The function should return NaN if X and Y does not have the same size or does not have minimum number of elements $($note that for linear fitting we need at least $2$ points$).$ The following steps can be used to find the equation of line of best fit based on least square method.

Step$-1$: Calculate the mean of the $x-$values and the mean of the $y-$values.

$\stackrel{}{x}=\frac{x_1+x_2+\text{c}\text{d}\text{o}\text{t}\text{s}+x_n}{n}$ and $\frac{?}{\text{b}\text{a}\text{r}}(Y)=\frac{y_1+y_2+\text{c}\text{d}\text{o}\text{t}\text{s}+y_n}{n}$

Step$-2$: the following formula gives the slope $($m$)$ of the line of best fit,

$m=\frac{(x_1-(\stackrel{}{x}))(y_1-(\frac{?}{\text{b}\text{a}\text{r}}(Y)))+(x_2-(\stackrel{}{x}))(y_2-(\frac{?}{\text{b}\text{a}\text{r}}(Y)))+\text{c}\text{d}\text{o}\text{t}\text{s}+(x_n-(\stackrel{}{x}))(y_n-(\frac{?}{\text{b}\text{a}\text{r}}(Y)))}{(x_1-(\stackrel{}{x}){)}^2+(x_2-(\stackrel{}{x}){)}^2+\text{c}\text{d}\text{o}\text{t}\text{s}+(x_n-(\stackrel{}{x}){)}^2}$

Step$-3$: compute the $y-$intercept $($b$)$ of the line by using the below formula,

$b\frac{?}{b}=ar(Y)-m\stackrel{}{x}$

Save your completed program as XY$.f95$ and upload it$,$ also Copy$-$&$-$paste it into the provided space below.

For an online FORTRAN compiler click here. A list of Fortran$90$ intrinsic functions can be found here or here.