```{r global_options, include=FALSE}
library(knitr)
opts_chunk$set(fig.align="center", fig.height=3, fig.width=4)
```
## In-class worksheet 11
**Feb 25, 2020**

In this worksheet, we will use the library tidyverse and ggthemes:
```{r message=FALSE}
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:
```{r}
# 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.
```{r}
# 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.

```{r}
# your R code goes here
```

Make a density plot that shows how the two species are separated by the linear predictor.
```{r}
# 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.
```{r}
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
)
```

```{r}
# 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.

```{r}
# your R code goes here
```

Now do the same calculation for versicolor.
```{r}
# 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?
```{r}
# your R code goes here
```
