In the article Application of Statistical Design in the Leaching Study of Low-Grade

Chapter 8, Problem 5

(choose chapter or problem)

In the article "Application of Statistical Design in the Leaching Study of Low-Grade Manganese Ore Using Aqueous Sulfur Dioxide" (P. Naik, L. Sukla, and S. Das, Separation Science and Technology, 2002:1375-1389), a fitted model for predicting the extraction of manganese in \(\%\ (y)\) from particle size in mm \((x_1)\), the amount of sulfur dioxide in multiples of the stoichiometric quantity needed for the dissolution of manganese \((x_2)\), and the duration of leaching in minutes \((x_3)\) is given as

\(y=56.145-9.046 x_{1}-33.421 x_{2}+0.243 x_{3}-0.5963 x_{1} x_{2}-0.0394 x_{1} x_{3}+0.6022 x_{2} x_{3}+0.6901 x_{1}^{2}+11.7244 x_{2}^{2}-0.0097 x_{3}^{2}\)

There were a total of  observations, with  and
a. Predict the extraction percent when the particle size is , the amount of sulfur dioxide is , and the duration of leaching is 20 minutes.

b. Is it possible to predict the change in extraction percent when the duration of leaching increases by one minute? If so, find the predicted change. If not, explain why not.

c. Compute the coefficient of determination \(R^2\).

d. Compute the  statistic for testing the null hypothesis that all the coefficients are equal to  Can this hypothesis be rejected?

Equation Transcription:

Text Transcription:

% (y)

(x_1)

(x_2)

(x_3)

y=56.145-9.046x_1-33.421x_2-0.5963x_1x_2-0.0394x_1x_3+0.6022x_2x_3+0.6901x_1^2+11.7244x_2^2-0.0097x_3^2

n=27

SSE=209.55

SST=6777.5

R^2