In an experiment to determine factors related to weld toughness, the Charpy V-notch

Chapter 8, Problem 1

(choose chapter or problem)

In an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in \(\mathrm {f t \cdot l b}\ (y)\) was measured for 22 welds at \(0^{\circ} \mathrm{C}\), along with the lateral expansion at the notch in \(\%~\left(x_{1}\right)\), and the brittle fracture surface in \(\%~\left(x_{2}\right)\). The data are presented in the following table.

y	\(x_1\)	\(x_2\)	y	\(x_1\)	\(x_2\)	y	\(x_1\)	\(x_2\)
32	20.0	28	27	16.0	29	25	14.6	36
39	23.0	28	43	26.2	27	25	10.4	29
20	12.8	32	22	9.6	32	20	11.6	30
21	16.0	29	22	15.2	32	20	12.6	31
25	10.2	31	18	8.8	43	24	16.2	36
20	11.6	28	32	20.4	24	18	9.2	34
32	17.6	25	22	12.2	36	28	16.8	30
29	17.8	28

a. Fit the model \(y=\beta_{0}+\beta_{1} x_{1}+\varepsilon\). For each coefficient, test the null hypothesis that it is equal to 0.

b. Fit the model \(y=\beta_{0}+\beta_{1} x_{1}+\varepsilon\). For each coefficient, test the null hypothesis that it is equal to 0.

c. Fit the model \(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\varepsilon\). 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?