---
title: "Graphing Residuals"
date: 'Last compiled: `r format(Sys.time(), "%A, %B %d, %Y - %X.")`'
author: 'Alan T. Arnholt'
output: 
    bookdown::html_document2
---

```{r label = "setup", include = FALSE, message = FALSE}
library(ggplot2)
knitr::opts_chunk$set(echo = TRUE, comment = NA, fig.align = "center", warning = FALSE, message = FALSE)
```

# (APPENDIX) Appendix A {-}

## Residuals

The $i^{th}$ residual is defined as $\hat{\epsilon}_i = y_i - \hat{y}_i$.


```{r}
library(dplyr)
library(PASWR2)
head(HSWRESTLER)
null <- lm(hwfat ~ 1, data = HSWRESTLER)
summary(null)
HSWRESTLER %>% 
  summarize(Intercept = mean(hwfat))
slr <- lm(hwfat ~ abs, data = HSWRESTLER)
summary(slr)
```

* Use the function `augment` from the `broom` package

```{r}
library(broom)
slr %>% 
  augment() %>% 
  head() %>% 
  round(3)
NDF <- slr %>% 
  augment()
```

## Graphing

```{r}
ggplot(data = NDF, aes(x = abs, y = hwfat)) + 
  geom_point(color = "purple") + 
  theme_bw() + 
  geom_smooth(method = "lm", se = FALSE, color = "gray") + 
  geom_segment(aes(x = abs, xend = abs, y = hwfat, yend = .fitted), size = 0.25)
```

```{r}
ggplot(data = NDF, aes(x = abs, y = hwfat)) + 
  geom_point(color = "purple") + 
  theme_bw() + 
  geom_line(aes(x = abs, y = .fitted), color = "gray") + 
  geom_segment(aes(x = abs, xend = abs, y = hwfat, yend = .fitted), size = 0.25)
```


```{r}
ndf1 <- augment(slr)
ndf2 <- augment(null)
ndf2$abs <- HSWRESTLER$abs
ndf <- bind_rows(ndf1, ndf2) %>% 
  mutate(model = rep(c("slr", "null"), each = 78)) 
DT::datatable(ndf)
```

```{r, fig.width = 8}
ggplot(data = ndf, aes(x = abs, y = hwfat)) +
  facet_grid(.~ model) + 
  geom_line(aes(x = abs, y = .fitted), color = "gray") + 
  theme_bw() + 
  geom_segment(aes(x = abs, xend = abs, y = hwfat, yend = .fitted), size = 0.25, linetype = "dotted") + 
  geom_point(color = "lightblue") 
```

### Something Else