Best subset vs stepwise, number of models created

num_mods_created.Rmd

``` r
library(tidyverse)

# as k increases from 1:p, see number of models created
p <- 10
map_dbl(1:p, ~ choose(.x, c(1:p)) %>% sum()) %>%
  enframe(name = NULL) %>%
  rename(best_subset = value) %>%
  mutate(p = 1:p,
         stepwise = 1 + p * (p + 1) / 2) %>%
  ggplot(aes(x = p)) +
  geom_line(aes(y = best_subset, colour = "best_subset"), size = 2) +
  geom_line(aes(y = stepwise, colour = "stepwise"), size = 2) +
  labs(title = "As p increases, number of models created increases", y = "Number of models created") +
  theme(text = element_text(size = 20))
```

![](https://i.imgur.com/YsrzXdp.png)

<sup>Created on 2019-02-05 by the [reprex package](https://reprex.tidyverse.org) (v0.2.1)</sup>