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 + β₁x₁ + β₂x₂ + β₃x₃. 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 x₁ is a useful predictor of rate of conversion y. Use α = .05. 

c. Construct a 95% confidence interval for β₂. Interpret the interval.

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y = Rate of conversion of MEA to EDA X1 = Atom ratio of metal used in the experiment x2 = Reduction temperature Si if high acidity support used X3 10 if low acidity support used %3D