After a manufacturer closed an old assembly plant, it re-trained its production employees to use new machines in a more highly automated robotic facility. The automated facility allows the plant to fill small orders of customized parts rather than turn out identical copies. After a weeklong training period, a group of these long-time employees were put to work.
Another group of workers were new hires that did not undergo this training. In a study of the value of this training program, an analyst regressed the number of items produced on the time required (in minutes) for completion of the order. The data are shown in this plot; trained employees are colored red.

(a) If we fit a separate equation to each group, then what is the interpretation of the intercept in either fit? Include the units as part of your description. What do these intercepts tell you about the training?
(b) What is the interpretation of the slopes in both regressions? Include the units as part of your description and relate these slopes to the training program.
(c) Will an analysis of covariance require an inter- action term, or can you skip this step and only fit a dummy variable to distinguish the two groups?

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