Impurities in the form of iron oxides lower the

economic value and usefulness of industrial miner$-$

als, such as kaolins, to ceramic and paper$-$processing

industries. A $2^4$ experiment was conducted to assess

the effects of four factors on the percentage of iron re$-$

moved from kaolin samples $("$Factorial Experiments

in the Development of a Kaolin Bleaching Pro$-$

cess Using Thiourea in Sulphuric Acid Solutions,"

Hydrometallurgy, $1997$: $181-197).$ The factors and

their levels are displayed in the following table:

The data from an unreplicated $2^4$ experiment is

given in the table below:

a$.$ Calculate all main effects and two$-$factor inter$-$ action effects for this experiment.

b$.$ Create a probability plot of the effects. Which effects appear to be important?

c$.$ Which settings $($high or low$)$ of the factors in part $($b$)$ lead to maximizing the percentage of iron extracted?

d$.$ Write a model for predicting iron extraction per$-$ centage from the factors identified in part $($b$).$