Brodnjak-Vonina et al. (2005) develop a methodology for food laboratories to determine the type of oil from a sample. In their procedure, they used a gas chromatograph (an instrument that separate chemicals in a sample) to measure seven different fatty acids in an oil. These measurements would then be used to predict the type of oil in a food samples. To create their model, they used 96 samples2 of seven types of oils. These data can be found in the caret package using data(oil). The oil types are contained in a factor variable called oilType.

a).Use the sample function in base R to create a completely random sample of 60 oils. How closely do the frequencies of the random sample match the original samples? Repeat this procedure several times of understand the variation in the sampling process

b.Use the caret package function createDataPartition to create a stratified random sample. How does this compare to the completely random samples?

c.With such a small samples size, what are the options for determining performance of the model? Should a test set be used?

(d) One method for understanding the uncertainty of a test set is to use a confidence interval. To obtain a confidence interval for the overall accuracy, the based R function binom.test can be used. It requires the user to input the number of samples and the number correctly classified to calculate the interval. For example, suppose a test set sample of 20 oil samples was set aside and 76 were used for model training. For this test set size and a model that is about 80 % accurate (16 out of 20 correct), the confidence interval would be computed using