Q$6(25$ pts$).$ You are provided with data from a series of experimental runs in a chemical reactor. The objective is to optimize the reaction rate by varying three factors: reaction temperature, catalyst concentration, and stirring speed. Each factor is tested at two levels, high and low.

Data Provided:

$\backslash$table$[[$Run$,\backslash$table$[[$Temperature$],[($High$/$Low$)]],\backslash$table$[[$Catalyst Concentration$],[($High$/$Low$)]],\backslash$table$[[$Stirring Speed$],[($High$/$Low$)]],\backslash$table$[[$Reaction$],[$Rate$]]],[1,$Low,Low,Low,$50],[2,$Low,Low,High,$55],[3,$Low,High,Low,$65],[4,$Low,High,High,$70],[5,$High,Low,Low,$60],[6,$High,Low,High,$65],[7,$High,High,Low,$80],[8,$High,High,High,$85]]$

Use the data above to perform a two$-$level factorial ANOVA. Calculate the mean squares for each factor and their interactions.

Determine the F$-$values to test the statistical significance of the model $($Note: Select the top three factors or interactions based on the highest SS values$).$