The "techies" in the laboratory have been lobbying you and the management in general, to include just one more laboratory step. They think it's a good idea., although you have some doubt because of one of them is known to be good friends with the founder of the startup biotechnology firm that makes the reagent that is used in the reaction. But if adding this step works as expected, it could help immensely in reducing production costs. The trouble is, the test results just came back and they don't look so good. Discussion at the upcoming meeting between the technical staff and management will be spirited, so you have decided to take a look at the data. Your firm is anticipating Government approval from the Food and Drug Administration (FDA) to market a new medical diagnostic test made possible by monoclonal antibody technology, and you are a part of the team in charge of production. Naturally the team has been investigating ways to increase production yields or lower costs. The proposed improvement is to insert yet another reaction as intermediate purifying procedure. This is good because it focuses resources down the line on the particular product you want to produce. But it shares the problem of any additional step in the laboratory; one more manipulation, one more intervention, one more way of something to go wrong. In this particular case, it has been suggested that while small amounts of the reagent may be helpful, trying to purify too well will actually decrease the yield and increase the cost. The design of the test was to have a series of test production runs, each with a different amount of purifier, including one test run with the purification step completely omitted (0 purifier). The order of the test was randomized so that at any time trends would not be mistakenly interpreted as being due to purification. Following are the data of the test.

Amount of purifier __________ Observed yield

0 .......................................... 13.39

1.......................................... 11.86

2 .......................................... 27.93

3 .......................................... 35.83

4 .......................................... 28.52

5 .......................................... 41.21

6 .......................................... 37.07

7 .......................................... 51.07

8 .......................................... 51.69

9 .......................................... 31.37

10 .......................................... 21.26

1. Report a scatter plot of amount of purifier and yield. What kind of association you observe? Write down your observations. 2. Fit a linear regression model. Does the amount of purifier have a significant effect on yield according to the regression analysis results? Report and interpret estimated model parameters (intercept & slope), ANOVA and t test results along with R2.

3. Based on this analysis alone, would you be likely to recommend including a purification step in the production process?

4. What would you recommend? Are there any other considerations that might change your mind?