What is being tested for in the following code and analysis?

a$)$ What is p for the mathematical formulation used in the code below for the analysis?

b$)$ What conclusions can you make from the plot below? Give justification for your answer.

c$)$ Compare the plot produced by proc sgplot data$=$ chiplot at the end of this question below with the plot reported in previous question. What can you conclude about the distributions by comparing the plots?

Left image is previous question, right image is plot from this question.

Code used:

proc iml;

use Dataset$\_$new;

reset print;

read all var $\{$x$1\_$x$2$ x$1\_$x$4$ x$2\_$x$3\}$ into x;

centre $=$ mean$($x$)$

cov $=$ cov$($x$)$

cor $=$ corr$($x$)$;

y $=$ t$($x$-$centre$)$;

d$2=$ t$($y$)*$inv$($cov$)*$y;

mahala $=$ vecdiag$($d$2)$;

ranks $=$ rank$($mahala$)$;

p $=$ ncol$($x$)$;

n $=$ nrow$($x$)$;

f$0=($ranks$-0\mathrm{.}5)/$n;

chiq $=$ cinv$($f$0,$p$)$;

chiplot $=$ mahala $||$ chiq;

create chiplot from chiplot$[$colnamme $=\{\text{'}$MAHDIST$\text{'}$ 'CHISQ'$\}]$;

append from chiplot;

quit;

proc sgplot data $=$ chiplot;

scatter y $=$ MAHDIST x $=$ CHISQ;

run;