An article in Process Biochemistry (Dec. 1996, Vol. 31(8), pp. 77-785) presented a 2^7€“3fractional factorial to perform optimization of manganese dioxide bioleaching media. The data are shown in the following table.

The factors and levels are shown in the following table.

(a) Write down the complete defining relation and the aliases from the design.

(b) Estimate the main effects.

(c) Plot the effect estimates on normal probability paper and interpret the results

(d) Conduct a residual analysis.

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Manganese Extraction Yield (%) 99.0 Runs 1 A -1 -1 -1 -1 -1 -1 -1 2 1 1 -1 97.4 1 -1 -1 97.7 -1 -1 90.0 4 -1 100.0 98.0 1 90.0