Chapter 8.3, Problem 4E

An engineer measures a dependent variable y and independent variables x₁, x₂, and x₃. MINITAB output for the model y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε is presented as follows.

Of the following, which is the best next step in the analysis? Explain your reasoning.

1. i. Add interaction terms $x_1{x}_2$ and $x_2{x}_3$ to try to find more variables to put into the model.
2. ii. Add the interaction term $x_1{x}_3$ to try to find another variable to put into the model.
3. iii. Nothing needs to be done. This model is tine.
4. iv. Drop $x_1$ and $x_3$, and then perform an F test.
5. v. Drop $x_2$, and then perform an F test.
6. vi. Drop the intercept (Constant), since it has the largest P-value.