Question

Part 3 (16 pts): Building a new model After seeing the analysis results, the client wondered if you can help design a better experiment to include study the microbial environment for C. elegans. Since you have study to no knowledge on microbiology, you convinced the client to conduct a pilot gather information about some bacteria that may be relevant with C. elegans. The client came back with a new set of data that includes measurements of C. elegans, Enterobacter, Pseudomonas, Acetobacter, Gluconobacter, Acetogluconobac- ter, Flavobacterium, Wautersiella, Sphingobacterium, Lactobacillus, Lacto- coccus, Leuconostoc. You now need to help the client to select variables that should be included in the new model, and thus the client can measure their densi- ties in the new experiment. Recall that the primary question of interest is the association between the density of Gluconobacter and the density of C. elegans. Also, measuring the density of one type of bacteria can be costly, and you want to help minimize the cost of experiments for your client. 1. As a first attempt, you draw many pairwise scatter plots, of which four are pro- vided below. (a) (6 pts) Based on these plots, do you think we need to include the density of Pseudomonas in the model? Justify your answer. (b) (6 pts) Based on these plots, do you think we need to include the density of Flavobacterium in the model? Justify your answer 2. (4 pts) The client is also interested in building a prediction model for the density of C. elegans given the densities of various bacteria. How will you select the vari- ables (densities of some bacterias) to include in the model given the pilot data?

Answer 1

1.

(a) Yes, we need to include the density of Pseudomonas because the scatterplot between Gluconobacter and Pseudomonas seems linear and the scatterplot between Celegans and Pseudomonas is also linear.

(b) No, we don’t need to include the density of Flavobacterium because the scatterplot between Gluconobacter and Flavobacterium seems linear and the scatterplot between Celegans and Flavobacterium is also linear.

2. The variables which are correlated with Celegans will be selected to include in the model.