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.

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

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Ху Ху x2 32 20.0 28 27 16.0 29 25 14.6 36 39 23.0 28 43 26.2 27 25 0.4 29 20 12.8 32 22 21 25 10.2 31 20 11.6 9.6 32 2016 30 16.0 29 22 15.2 32 20 12.6 31 8.8 43 24 16.2 36 34 18 32 204 24 32 17.6 25 22 12.2 36 28 16.8 30 28 9.2 29 17.8 28