---
title: "Lecture 5 Exercises"
author: "Your Name"
output: html_document
---
```{r setup, message = FALSE, warning = FALSE, echo=FALSE}
knitr::opts_chunk$set(message = FALSE, warning = FALSE, dev="svg", tidy=TRUE,  tidy.opts = list(only.comment=TRUE,  width.cutoff=80))
library(summarytools)
library(dplyr)
```

We're going back to the COVID-19 data that we used before, we need to load it first.  (It's also available locally in the RStudio.cloud instance or from [my website](https://quantoid.net/files/reg3/counties.rda))

```{r}
library(stringr)
load(file("https://quantoid.net/files/reg3/counties.rda"))
```

This makes an object in your workspace called `counties`.  To remind, here's a summary of the data: 

```{r, results='asis', eval=FALSE}
counties %>% 
  select(-c("fips", "NAME", "date", "state", "st")) %>% 
  dfSummary(., plain.ascii=FALSE)
```

I want you to use the data to answer the following questions. 

### Question 1

Using the three different models you estimated in the `lecture7_exercises.rmd` file,  
  - Use all ridge regression, the LASSO, the elastic net and the adaptive LASSO on each model. 
  - Now, use these tools on the combined variables in all three models. 
  - What do the results tell you and how are they different/similar to what you found in the last set of exercises?

### Question 2

Use the tools mentioned above to predicte `cases` using all of the available covariate data. 
  - What do you find? 
  - How does this result differ from what you when using model averaging?
  
  
