A quantity p varies with another quantity q according to the formula

$p^2=\frac{1}{aq+b}$

The following data are taken for p and q:

q $1\mathrm{.}002\mathrm{.}003\mathrm{.}005\mathrm{.}00$

p $0\mathrm{.}950\mathrm{.}590\mathrm{.}430\mathrm{.}35$

$($a$)$ What plot would yield a straight line if the given equation is correct?

$($b$)$ Estimate a and b by the method of least squares