## 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`