Several bench scale reactors were operated in the laboratory as completely mixed reactors with recycle to determine kinetic coefficients for a wastewater.

All reactors were operated at the same detention time $$ of $4h$ and initial soluble substrate concentration of $600$mgBO$\frac{D}{L}.$ The experimental data are provided below:

$\backslash$table$[[$Reactor$,$S$,$mgBOD$/$L$,$x$,$mgVSS$/$L$,\backslash$tau $\_($c$),$d$],[1,350,310,0\mathrm{.}45],[2,230,496,0\mathrm{.}50],[3,190,608,0\mathrm{.}55],[4,125,759,0\mathrm{.}60],[5,70,1030,0\mathrm{.}75],[6,45,1406,1\mathrm{.}05]]$

Using Excel, perform a linear regression on the provided data to calculate the sludge yield coefficient, $Y,$ in $mgVS\frac{S}{m}g$ BOD, and the endogenous respiration coefficient, $k_e,$ in $\frac{1}{d}.$ Assume the settling tank volume is negligible compared to the reactor volume. Present regression graph and include best$-$fit equation and coefficient of determination.