$6\mathrm{.}24)$ Please help! Use PYTHON code for answering the $3$ questions. $6\mathrm{.}24$ Consider a variation of the bottle filling experiment

from Example $5\mathrm{.}3.$ Suppose that only two levels of carbona$-$

tion are used so that the experiment is a $2^3$ factorial design

with two replicates. The data are shown in Table P$6\mathrm{.}3.$

TABLE P$6\mathrm{.}3$

Fill Height Experiment from Problem $6\mathrm{.}24$

$($a$)$ Analyze the data from this experiment. Which factors

significantly affect fill height deviation?

$($b$)$ Analyze the residuals from this experiment. Are there

any indications of model inadequacy?

$($c$)$ Obtain a model for predicting fill height deviation in

terms of the important process variables. Use this model

to construct contour plots to assist in interpreting the

results of the experiment.