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# Regression analysis

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1. The following table lists the percent yields of 25 consecutive batches (read across rows) Construct a time-sequence plot and comment on its appearance.
72.4 75.3 72.7 74.2 75.6 75.0 73.3 73.1 74.4 77.5
75.8 74.0 73.2 74.8 76.2 72.7 68.2 79.1 73.8 75.5
74.7 75.7 72.9 72.1 77.7

1b. Construct a dot diagram and calculate the summary statistics
Sample Moisture Weight Sample Moisture Weight
1 9.2 8.19 11 8.9 8.17
2 8.6 8.15 12 9.5 8.16
3 8.5 8.10 13 8.7 8.12
4 8.9 8.15 14 8.2 8.06
5 9.9 8.23 15 8.3 8.10
6 8.0 8.07 16 9.7 8.22
7 8.9 8.11 17 9.1 8.13
8 9.1 8.16 18 9.1 8.17
9 9.4 8.19 19 8.5 8.08
10 8.4 8.11 20 9.7 8.21

2. In the production of shampoo it has long been speculated that the pH level is a major factor in controlling the color of the product. The following data were obtained by sampling several batches and determining their pH and their "B-color." Interpret the data. Construct a scatter plot and calculate the correlation coefficient.

Batch pH B-Color
1 6.4 5.50
2 6.4 6.33
3 6.6 6.09
4 6.3 3.54
5 6.5 7.14
6 6.5 9.41
7 6.4 8.61
8 6.4 9.81
9 6.4 7.46
10 6.5 6.99
11 6.3 6.29
12 6.5 8.32
13 6.3 9.81
14 6.4 9.95
15 6.3 8.48
16 6.5 9.84
17 6.5 8.57
18 6.5 9.90
19 6.4 9.53
20 6.4 8.86
21 6.3 8.70
22 6.5 5.40
23 6.3 9.40
24 6.5 8.72
25 6.4 8.72

3. Among the 120 defects from a lens-polishing operation, we found 12 lenses with incorrect dimensions, 33 scarred lenses, 8 cracked lenses, 15 unfinished lenses, 44 poorly coated lenses, and 8 where the defect could not be classified ("other"). Construct a Pareto diagram. Assuming that each type of defect is equally costly, which defect would you
attack first?

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#### Solution Preview

Please see the attachments.

Statistics
1. The following table lists the percent yields of 25 consecutive batches (read across rows) Construct a time-sequence plot and comment on its appearance.
72.4 75.3 72.7 74.2 75.6 75.0 73.3 73.1 74.4 77.5 75.8 74.0 73.2 74.8 76.2 72.7 68.2 79.1 73.8 75.5 74.7 75.7 72.9 72.1 77.7

The sequence chart suggests that the percent yields are varying around the value 75. Thus 75 can be considered as the mean yield.

1b. Construct a dot diagram and calculate the summary statistics
Sample Moisture Weight Sample Moisture Weight
1 9.2 8.19 11 8.9 8.17
2 8.6 8.15 12 9.5 8.16
3 8.5 8.10 13 8.7 8.12
4 8.9 8.15 14 8.2 8.06
5 9.9 8.23 15 8.3 8.10
6 8.0 8.07 16 9.7 8.22
7 8.9 8.11 17 9.1 8.13
8 9.1 8.16 18 ...

#### Solution Summary

Step-by-step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.

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