$**$Please use RStudio & R Coding! Please show code!

Problem $6\mathrm{.}3$ More on parameter fitting, In the class, we illustrated how to perform parameter fitting of the

Lotka$-$Voiterra model against a time$-$series data set. In that example, we detined an error function by Sum of

square differences $($SSD$)$ between model and datz. Here, you are asked to define a different error criterion, the

sum of the absolute values $($not ther squares$).$ Try a few $()$ initial parameters $($a$,$ b$,$ c$,$ d values, e$.$g$.,$ the

initial conditions we have tried in the class$),$ and perform nonlinear minimization.

For each case,

$(1)$ Plot the time trajectories together with the data;

$(2)$ Show the parameters you obtained from the optimization;

$(3)$ Show the final error values.

And compare your results $($qualitatively$)$ with those using the original algorithm with SSD as the error function.

Notes: If you use R$,"$O$3$D$.$Rmd$"$ from Oanvas is a good starting point. If you use Matlab, you can start from the

code from the lecture notes $($search "fitjlotka$\_$volterta.m$").$ If you use Python or other languages, you then

have to wilte your own script to perform ertor minimization.

The time$-$series data can be found in the csv file $"$LV$\_$data.csv$".$

Ivdata $=$ read.osv$("$IV$\_$data.osv", header $=7)[,2$:$4]$

kn$1$tr::kable$($lvdata$,$ ool,nemes $=$ o$("$Year$",$ "Hare $($x$1000)".$ "Iyns $(\%1000)"))$