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
|
8.8
|
10.0
|
0.091
|
51.609
|
|
51.9
|
8.8
|
10.0
|
0.291
|
51.609
|
|
50.0
|
8.1
|
7.1
|
-0.517
|
50.517
|
|
50.5
|
8.1
|
9.0
|
0.790
|
49.710
|
|
50.0
|
8.1
|
7.1
|
-0.517
|
50.517
|
|
49.7
|
8.1
|
9.0
|
-0.010
|
49.710
|
|
50.6
|
8.1
|
9.0
|
0.890
|
49.710
|
|
47.7
|
7.2
|
7.2
|
0.214
|
47.486
|
|
47.1
|
7.3
|
7.8
|
-0.464
|
47.564
|
|
45.0
|
7.3
|
11.8
|
-0.864
|
45.864
(Continued)
|
|
Strength
|
Manganese
|
Thickness
|
Residual
|
Fitted Value
|
|
47.6
|
7.3
|
8.0
|
0.121
|
47.479
|
|
45.7
|
7.3
|
11.8
|
-0.164
|
45.864
|
|
47.0
|
7.3
|
8.7
|
-0.181
|
47.181
|
|
45.7
|
7.3
|
11.7
|
-0.206
|
45.906
|
|
48.8
|
7.3
|
8.7
|
1.619
|
47.181
|
|
45.8
|
7.3
|
7.8
|
-1.764
|
47.564
|
|
48.5
|
7.3
|
9.0
|
1.446
|
47.054
|
|
48.6
|
7.6
|
7.8
|
0.040
|
48.560
|