Feb 23, 2016

# 1. Fitting a logistic regression model to the iris data set

We will work with the iris data set. Specifically, with a subset of the data that consists only of the species virginica and versicolor:

# make a reduced iris data set that only contains virginica and versicolor species
iris.small <- filter(iris, Species %in% c("virginica", "versicolor"))

Fit a logistic regression model to the iris.small data set. Then successively remove predictors until only predictors with a p value less than 0.1 remain.

# your R code goes here

Make a plot of the fitted probability as a function of the linear predictor, colored by species identity. Hint: you will have to make a new data frame combining data from the fitted model with data from the iris.small data frame.

# your R code goes here

Make a density plot that shows how the two species are separated by the linear predictor.

# your R code goes here

# 2. Predicting the species

Assume you have obtained samples from three plants, with measurements as listed below. Predict the likelihood that each of these plants belongs to the species virginica.

plant1 <- data.frame(Sepal.Length=6.4, Sepal.Width=2.8, Petal.Length=4.6, Petal.Width=1.8)
plant2 <- data.frame(Sepal.Length=6.3, Sepal.Width=2.5, Petal.Length=4.1, Petal.Width=1.7)
plant3 <- data.frame(Sepal.Length=6.7, Sepal.Width=3.3, Petal.Length=5.2, Petal.Width=2.3)
# your R code goes here

# 3. If this was easy

Pick a cutoff predictor value at which you would decide that a specimen belongs to virginica rather than versicolor. Calculate how many virginicas you call correctly and how many incorrectly given that choice.

# your R code goes here

Now do the same calculation for versicolor.

# your R code goes here

If we define a call of virginica as a positive and a call of versicolor as a negative, what are the true positive rate (sensitivity, true positives divided by all possible positives) and the true negative rate (specificity, true negatives divided by all possible negatives) in your analysis?

# your R code goes here