Animations are excellent tools for teaching and building intuition. Here we show how a LOESS fit (with a 1-degree polynomial) is constructed, by performing a weighted regression in many overlapping windows.

First, we see how the broom packageâ€™s `augment`

function is useful for plotting a LOESS fit.

```
library(lattice)
library(ggplot2)
library(broom)
theme_set(theme_bw())
mod <- loess(NOx ~ E, ethanol, degree = 1, span = .75)
fit <- augment(mod)
ggplot(fit, aes(E, NOx)) +
geom_point() +
geom_line(aes(y = .fitted), color = "red")
```

We now need to compute a separate regression centered around each point on the graph. broomâ€™s `inflate`

function is useful for this, followed by some dplyr manipulation to filter the distant ones (using a span of .75). Notice that we filter out all but the 75% closest points, and then calculate tricube weights, just like the loess function does, on those points.

```
library(dplyr)
dat <- ethanol %>%
inflate(center = unique(ethanol$E)) %>%
mutate(dist = abs(E - center)) %>%
filter(rank(dist) / n() <= .75) %>%
mutate(weight = (1 - (dist / max(dist)) ^ 3) ^ 3)
dat
```

```
## Source: local data frame [5,478 x 6]
## Groups: center [83]
##
## center NOx C E dist weight
## (dbl) (dbl) (dbl) (dbl) (dbl) (dbl)
## 1 0.535 3.741 12.0 0.907 0.372 0.38324129
## 2 0.535 2.295 12.0 0.761 0.226 0.82699305
## 3 0.535 1.498 12.0 1.108 0.573 0.00000000
## 4 0.535 2.881 12.0 1.016 0.481 0.06815599
## 5 0.535 3.120 9.0 1.001 0.466 0.09868125
## 6 0.535 2.358 12.0 1.042 0.507 0.02901265
## 7 0.535 3.669 12.0 0.930 0.395 0.30402352
## 8 0.535 1.192 18.0 0.601 0.066 0.99542253
## 9 0.535 0.926 7.5 0.696 0.161 0.93491730
## 10 0.535 1.590 12.0 0.686 0.151 0.94609661
## .. ... ... ... ... ... ...
```

We are now ready to create an animation, where each frame uses a different center. The most important layer here is the `geom_smooth`

step with the `weight = weight`

aesthetic. This does all the work of adding a best-fit line from the weighted regression. We also add a `geom_vline`

to show the current center.

```
p <- ggplot(dat, aes(E, NOx)) +
geom_point(aes(alpha = weight, frame = center)) +
geom_smooth(aes(group = center, frame = center, weight = weight), method = "lm", se = FALSE) +
geom_vline(aes(xintercept = center, frame = center), lty = 2) +
geom_line(aes(y = .fitted), data = fit, color = "red")
library(gganimate)
gg_animate(p)
```