Our team at Tessier$-$Ashpool is working on a novel chromatography resin. Your team is tasked with estimating the Darcy permeability for this resin. After packing $3$ columns with resin, you apply three pressure drops to each column and measure the bulk outflow. The columns have a length of $10cm$ and a diameter of $1\mathrm{.}5cm.$ The chromatography fluid has a viscosity of $0\mathrm{.}002P{a}^{***}s.$

Does $k$ have a linear response to pressure?

Use the following data to determine a reasonable value for $k$ with a $95\%$ confidence interval.

$\backslash$table$[[$Q$,2\mathrm{.}5$kPa,$5\mathrm{.}0$kPa,$10$kPa