The computer operations department has a business objective of reducing the amount of time to fully update each subscriber’s set of messages in a special secure email system. A team designed a factorial experiment involving two factors, i.e., Interface and Media, with the goal of understanding the importance of these factors in explaining the variability in Update Time. The factor Interface has three levels, i.e., System I, System II, and System III, while the factor Media has two levels, i.e., Cable and Fiber. Consequently, there are 3x2=6 different factor-level combinations. Subscribers were randomly assigned to one of the 6 factor-level combinations and Update Time was recorded for each observation.
1. Analyze the experimental data. Report the ANOVA Table and comment on the importance of the two factors and their interaction in explaining the variability in Update Time.
2. If there are model terms with p-values > 0.05, drop them from the model and re-analyze the data under your reduced model. Refer to this as your final model.
3. Report and interpret the coefficient of determination, ? , for your final model.
4. What level(s) of the important factor(s) appears to produce the shortest Update Time?
| Subscriber ID | Update Time | Interface | Media |
| 1 | 4.56 | System I | Cable |
| 2 | 4.9 | System I | Cable |
| 3 | 4.18 | System I | Cable |
| 4 | 3.56 | System I | Cable |
| 5 | 4.34 | System I | Cable |
| 6 | 4.17 | System II | Cable |
| 7 | 4.28 | System II | Cable |
| 8 | 4 | System II | Cable |
| 9 | 3.96 | System II | Cable |
| 10 | 3.6 | System II | Cable |
| 11 | 3.53 | System III | Cable |
| 12 | 3.77 | System III | Cable |
| 13 | 4.1 | System III | Cable |
| 14 | 2.87 | System III | Cable |
| 15 | 3.18 | System III | Cable |
| 16 | 4.41 | System I | Fiber |
| 17 | 4.08 | System I | Fiber |
| 18 | 4.69 | System I | Fiber |
| 19 | 5.18 | System I | Fiber |
| 20 | 4.85 | System I | Fiber |
| 21 | 3.79 | System II | Fiber |
| 22 | 4.11 | System II | Fiber |
| 23 | 3.58 | System II | Fiber |
| 24 | 4.53 | System II | Fiber |
| 25 | 4.02 | System II | Fiber |
| 26 | 4.33 | System III | Fiber |
| 27 | 4 | System III | Fiber |
| 28 | 4.31 | System III | Fiber |
| 29 | 3.96 | System III | Fiber |
| 30 | 3.32 | System III | Fiber |
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