The model $y=mx^{2}$ is to be fit to the data given below.

$$\begin{array}{|cl|cI|}\hline &{x} & {1} & {\sqrt{2}} & {\sqrt{3}} \\ \hline &{y} & {2} & {5} & {8} \\ \hline \end{array}$$

Using linear regression, the value (rounded off to the second decimal place) of $m$ is _________