In-class worksheet 11

Feb 25, 2020

In this worksheet, we will use the library tidyverse and ggthemes:

library(tidyverse)
theme_set(theme_bw(base_size = 12)) # set default ggplot2 theme
library(ggthemes)

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 <- 
  iris %>%
  filter(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