---
title: "AE 05: Comparing two continuous variables"
author: "Your Name Here"
date: "Date Here"
format: html
---

Due Thursday, April 3.

## Learning goals

-   Use correlations to quantify linear association between two continuous variables.

-   Use visualization to dig deeper and understand what linear correlation is and isn't.

## Data: mtcars

Load the data by running the code:

```{r}
#| warning: false
#| message: false
data(mtcars)
library(tidyverse)
library(ggcorrplot)

```

Let's take a quick look at the contents:

```{r}
?mtcars
glimpse(mtcars)

```

Let's focus on a few variables:

-   mpg: miles per gallon (fuel efficiency)

-   cyl: number of cylinders (bigger/stronger engines often have more cylinders).

-   disp: displacement (cubic in.). The volume of the engine's cylinders (bigger/stronger engines often have larger displacement)

-   hp: horsepower, a measure of engine power, or the rate at which work is done.

-   drat: rear axle ratio. Lower generally means better fuel economy (mpg), higher means more towing power.

-   wt: weight of the car.

-   qsec: Time to complete a quarter mile (i.e. speed of car in a drag race).

Let's limit the data to just these variables, and then look again at the correlation plot (we saw the full correlation plot for all variables in lecture).

```{r}
data <- mtcars |>
  select(mpg, cyl, disp, hp, drat, wt, qsec)

corr <- round(cor(data), 1)
ggcorrplot(corr)
```

The darker red colors are higher correlations (close to 1), the darker purple correlations are lower correlations (close to -1), and the paler colors are smaller correlations (closer to 0).

Now, as an example, let's take one pair of variables and look at the linear correlation, as well as the scatter plot comparing the two values.

```{r}
cor(data$wt, data$mpg)
plot(data$wt, data$mpg)
```
Looks quite straightforward--they are strongly negatively correlated, and show a clear linear relationship. And it makes intuitive sense, a heavier car is going to have lower mpg because there is more mass for the engine to move.

## Exercise 1 - horsepower and quarter mile time

a. Using code from above, find the correlation between horsepower and quarter mile time, then make a scatter plot with horsepower on the x-axis, and quarter-mile time on the y-axis.
```{r}
# Correlation and scatter plot

# [type code here]
```

b. How would you interpret and explain the correlation and scatter plot you obtained?

\[type response here\]

## Exercise 2 — rear axle ratio and horsepower

I don't really know what rear axle ratio means aside from what I found online, that lower generally means better fuel economy (mpg), and higher means more towing power. With that in mind, let's look at one association.

a. Using code from above, find the correlation between rear axle ratio and horsepower. Then, make a scatter plot with horsepower on the x-axis, and rear axle ratio on the y-axis. Describe your findings from both the correlation, and graphical analysis.

```{r}
# Correlation and scatter plot

# [type code here]
```

\[type response here\]

b.  Based on the material in lecture, do you think the correlation coefficient is a good summary of the strength of relationship between these two variables? Why or why not?

\[type response here\]

## Submission

Render to PDF and submit on Canvas \> Assignments.