Polynomial Regression: Five measurements were performed to

determine the breaking distance, d$\_$i$,$ of a car at various speeds

$($v$\_$i $)($i$=1,2,3,4,5).$ The results were entered in Table $2\mathrm{.}1$

v$\_$i $($m$/$s$)1015202530$

d$\_$i $($m$)4\mathrm{.}59\mathrm{.}919\mathrm{.}228\mathrm{.}341\mathrm{.}0$

Table $2\mathrm{.}1$: Breaking distance d as a function of speed v

We assume that there is a quadratic relationship

d$\_$i$=$av$\_$i$^2+$b $(2\mathrm{.}1)$

between speed and breaking distance.