Solve it without using minitab $.$

$11-7.$ An article in the Tappi Journal $($March $1986)$ presented data on green liquor $N{a}_{2}S$ concentration $($in grams per liter$)$ and paper machine production $($in tons per day$).$ The data $($read from a graph$)$ follow:

$\backslash$table$[[y,40,42,49,46,44,48],[x,825,830,890,895,890,910]]$

$\backslash$table$[[y,46,43,53,52,54,57,58],[x,915,960,990,1010,1012,1030,1050]]$

$($a$)$ Fit a simple linear regression model with $y=$ green liquor $N{a}_{2}S$ concentration and $x=$ production. Find an estimate of ${}^2.$ Draw a scatter diagram of the data and the resulting least squares fitted model.

$($b$)$ Find the fitted value of $y$ corresponding to $x=915$ and the associated residual.

$($c$)$ Find the mean green liquor $N{a}_{2}S$ concentration when the production rate is $960$ tons per day.