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1. Refer to Exercise 1.
a. Find a 95% confidence interval for the coefficient of Manganese.
b. Find a 99% confidence interval for the coefficient of Thickness.
c. Can you conclude that β1 > 3? Perform the appropriate hypothesis test.
d. Can you conclude that β2 -0.1? Perform the appropriate hypothesis test.
2. The data used to fit the model in Exercise 1 are presented in the following table, along with the residuals and the fitted values. Plot the residuals versus the fitted values. Does the plot indicate that the linear model is reasonable? Explain.
Strength
Manganese
Thickness
Residual
Fitted Value
47.7
7.4
8.0
-0.111
47.811
50.9
8.8
10.0
-0.709
51.609
51.7
0.091
51.9
0.291
50.0
8.1
7.1
-0.517
50.517
50.5
9.0
0.790
49.710
49.7
-0.010
50.6
0.890
7.2
0.214
47.486
47.1
7.3
7.8
-0.464
47.564
45.0
11.8
-0.864
45.864
(Continued)
47.6
0.121
47.479
45.7
-0.164
47.0
8.7
-0.181
47.181
11.7
-0.206
45.906
48.8
1.619
45.8
-1.764
48.5
1.446
47.054
48.6
7.6
0.040
48.560
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