In a corrosion test, three types of materials are selected: Aluminium, Stainless Steel and Alloy. They are provided by three different

companies of BScope, Nippon Steel and Bao Steel. The obtained corrosion rate data is shown in Table Q$3\mathrm{.}1.$

Table Q$3\mathrm{.}1$ Corrosion rate $($micrometre$/$month$)$ now give me the following question answers: $($i$)$ Produce two bivariate plots: Corrosion rate versus material type $($x$1)$ and corrosion rate versus company $($x$2).$ Describe on the shape of each graph if it is approximately linear or nonlinear, and comment on what this indicates about the adequacy of the possible linear model,

corrosion rate, y $=\backslash$beta $0+\backslash$beta $1$ x$1+\backslash$beta $2$ x$2+$ e$.(6$ marks$)$

$($ii$)$ Build model and identify if there is evidence $($with a $=0\mathrm{.}05)$ indicating that either material type or company affects the corrosion rate. Find the p$-$value corresponding to each term that should be included in the model. $(5$ marks$)$

$($iii$)$ Is there a significant interaction effect? What conclusions can you draw about the model type that should be selected to model the data? $(5$ marks$)$

$($iv$)$ Fit an appropriate model relating the corrosion rate to material type and$/$or company. Write out the model determined. $(6$ marks$)$

$($v$)$ Plot and analyse the residuals from this experiment. Comment on the adequacy of the models you have considered. $($Save your plot into a report file and mark it as Q$3($v$)).(6$ marks$)$

$($vi$)$ Assume the model obtained in part $($iv$)$ is adequate, what material type and$/$or company would you recommend? $($Here$,$ the lower the response value, the better the material.$)(5$ marks$)$