Chapter 8.2, Problem 1E

In an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft·lb (y) was measured for 22 welds at 0°C, along with the lateral expansion at the notch in % (x₁), and the brittle fracture surface in % (x₂). The data are presented in the following table.

1. a. Fit the model y = β₀ + β₁x₁ + ε. For each coefficient, test the null hypothesis that it is equal to 0.
2. b. Fit the model y = β₀ + β₁x₂ + ε. For each coefficient, test the null hypothesis that it is equal to 0.
3. c. Fit the model y = β₀ + β₁x₁ + β₂x₂ + ε. For each coefficient, test the null hypothesis that it is equal to 0.
4. d. Which of the models in parts (a) through (c) is the best of the three? Why do you think so?