---
title: "HW 3: key"
format: pdf
editor: source
---

```{r}
#| message: false
#| echo: false
library(tidyverse)
library(spatstat)
```

## Question 1 (4 points)

Recall the elk dataset from HW 1. Investigate whether this dataset exhibits CSR. Justify your findings with a paragraph summary.

```{r, echo=T}
elk <- read_csv('https://raw.githubusercontent.com/Stat534/data/refs/heads/main/elk.csv')
```

## Question 2

In this question we are going to simulate and fit a dataset with spatial covariates.

### 2.1 (3 points)

Create a set of at least two spatial covariates that will be related to your intensity surface. Note you'll want to explore the `im()` function which allows you to create a pixel-image. Plot your spatial covariates.


### 2.2 (3 points)

Construct and plot your intensity surface, this should use the covariates from 2.2 and at least one of the x or y coordinate values.

### 2.3 (3 points)

Determine and justify whether your surface exhibits CSR.

### 2.4 (3 points)

Model your intensity surface and summarize your results. How close are your parameter estimates?

### 2.5 (3 points)

Compare how well your estimated intensity surface matches with the true generated intensity surface.
