Chapter 8, Problem 6SE

The data in Table SE6 (page 649) consist of yield measurements from many runs of a chemical reaction. The quantities varied were the temperature in °C (x₁), the concentration of the primary reactant in % (x₂), and the duration of the reaction in hours (x₃). The dependent variable (y) is the fraction converted to the desired product.

1. a. Fit the linear model $y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+\epsilon$.
2. b. Two of the variables in this model have coefficients significantly different from 0 at the 15% level. Fit a linear regression model containing these two variables.
3. c. Compute the product (interaction) of the two variables referred to in part (b). Fit the model that contains the two variables along with the interaction term.
4. d. Based on the results in parts (a) through (c), specify a model that appears to be good for predicting y from x₁ x₂, and x₃.
5. e. Might it be possible to construct an equally good or better model in another way?

TABLE SE6 Data for Exercise 6