---
title: "AE 07: Logistic regression"
author: "Your Name Here"
date: "Date Here"
format: html
---

In this application exercise, you will work with a **simulated environmental dataset** containing three variables:

-   `bird_presence`: whether a rare bird species was detected at a survey site (0/1)
-   `air_quality`: numeric index (higher = worse air quality)
-   `trees`: number of trees per hectare at the site
-   `wetland`: whether the site is a wetland (1 = yes, 0 = no)

You will:

1.  Fit a logistic regression model\
2.  Interpret a continuous coefficient\
3.  Interpret a binary or categorical coefficient\
4.  Predict a probability for a new site

## Computational setup

```{r}
#| message: false
#| warning: false
library(tidymodels)
library(kableExtra)
```

## Simulating the dataset

Run the following code to simulate the dataset.

```{r}
set.seed(9745)

n <- 200

air_quality <- rnorm(n, mean = 50, sd = 10)      # continuous predictor
trees <- rpois(n, lambda = 30)                   # count predictor
wetland <- rbinom(n, size = 1, prob = 0.4)       # binary predictor

# true model:
# logit(p) = -7 + 0.05*air_quality + 0.04*trees + 1.0*wetland
log_odds <- -7 + 0.05 * air_quality + 0.04 * trees + 1 * wetland
prob <- exp(log_odds) / (1 + exp(log_odds))

bird_presence <- rbinom(n, size = 1, prob = prob)

env_data <- data.frame(
  bird_presence,
  air_quality,
  trees,
  wetland
)

head(env_data)
```

## Exercise 1

Fit a logistic regression model predicting bird presence from air quality, trees, and whether the side was a wetland. Display the coefficient estimates table using `kable()`, rounding to 3 digits.

```{r}
# insert code here
```

## Exercise 2: Interpretation

Interpret the estimated coefficient for `air_quality` in terms of **odds**. (You can state in terms of a multiplicative change or a percent difference in odds.) (1–2 sentences)

\[type response here\]

## Exercise 3: Interpretation

Interpret the estimated coefficient for `wetland` in terms of **odds**. (You can state in terms of a multiplicative change or a percent difference in odds.) (1–2 sentences)

\[type response here\]

## Exercise 4: Prediction

Predict the **probability** of bird presence for a site with:

-   `air_quality` = 60

-   `trees` = 40

-   `wetland` = 1 (wetland site)

Use `predict(..., type = "response")`.

```{r}
# type code here
```