In this question, we will examine a Milk Production dataset.

A researcher has collected some data on daily milk production and classified it as low, medium or high. We are interested in whether baby birth weight, number of feeds (on average, per day) and mother concern (measure from 0 to 100) can aid in classifying maternal production.

(a) Discuss the assumptions of linear discriminant analysis as they relate to this data set. (3 marks)

(b) Using linear discriminant analysis, determine the hit rate when considering the variables baby birthweight, number of feeds and mother concern in trying to predict the outcome. (3 marks)

(c) Using the group means, describe the three outcomes and how they typically differ. (3 marks)

(d) How does this change if we say that the costs of mis-diagnosing the high or low production mothers are 5 times that of medium production.

i. What are the new priors? (2 marks)

ii. What is the new hit rate? (3 marks)

(e) Is linear discriminant analysis effective in this context?

Provide at least one visualisation to support your answer. (2 marks)

Note: Be sure to remove the randomness from the linear discriminant analysis analysis by setting the seed in your R-code.