The yield of a chemical process is related to the concentration of the reactant and the operating temperature. An experiment has been conducted with the following results.

The yield of a chemical process is related to the concentration of the reactant and the operating temperature. An experiment has been conducted with the following results.

(a) Suppose we wish to fit a main effects model to this data. Set up the X'X matrix using the data exactly as it appears in the table.

(b) Is the matrix you obtained in part (a) diagonal? Discuss your response.

(c) Suppose we write our model in terms of the "usual" coded variables

 

Set up the X'X matrix for the model in terms of these coded variables. Is this matrix diagonal? Discuss your response.

(d) Define a new set of coded variables

Set up the X'X matrix for the model in terms of this set of coded variables. Is this matrix diagonal? Discuss your response.

(e) Summarize what you have learned from this problem about coding the variables.

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Yield Concentration Temperature 81 1.00 150 89 1.00 180 83 2.00 150 91 2.00 180 79 1.00 150 87 1.00 180 84 2.00 150 90 2.00 180