A study was conducted at Union Carbide to identify the optimal catalyst preparation conditions in the conversion of monoethanolamine (MEA) to ethylenediamine (EDA), a substance used commercially in soaps. For each of 10 preselected catalysts, the following experimental variables were measured:

The data for the n = 10 experiments were used to fit the multiple regression model E(y) = β_{o} + β_{1}x_{1} + β_{2}x_{2} + β_{3}x_{3}. The results are summarized as follows:

a. Is there sufficient evidence to indicate that the model is useful for predicting rate of conversion y? Test using α = .01.

b. Conduct a test to determine whether atom ratio x_{1} is a useful predictor of rate of conversion y. Use α = .05.

c. Construct a 95% confidence interval for β_{2}. Interpret the interval.