130-Outside-of-the-normal.Rmd

# Outside of the normal

```{r include=FALSE}
SDSdata::sds_setup()
knitr::opts_knit$set('bookdown.internal.label' = FALSE)
```
About ranks, transformations, ...

Hooker and Yule paper, 1906

```{r}
load("data/Wheat_export.rda")

cor(export ~ price, data = Wheat_export)
cor(export ~ production, data = Wheat_export)
cor(rank(export)  ~ rank(price),  data = Wheat_export )
cor(rank(export)  ~ rank(production),  data = Wheat_export )
cor(diff(export)  ~ diff(price),  data = Wheat_export)
cor(diff(export)  ~ diff(production),  data = Wheat_export)
gf_point(export ~ price, data = Wheat_export)
gf_point(export ~ production, data = Wheat_export)
plot(diff(export)  ~ diff(price),  data = Wheat_export)
plot(diff(export)  ~ diff(production),  data = Wheat_export)
lm(diff(export)  ~ diff(production) + diff(price),  data = Wheat_export) %>%
  summary()
plot(rank(diff(export))  ~ rank(diff(price)),  data = Wheat_export)
plot(rank(diff(export))  ~ rank(diff(production)),  data = Wheat_export)
```

They computed indices, which seem to be the standardized annual differences.

```{r}

Indices  <- 
  with(Wheat_export,
       data.frame(export = diff(export),
                  price = diff(price),
                  production = diff(production))) %>%
  mutate(export = (export - mean(export))/sd(export),
         price = (price - mean(price))/sd(price),
         production = 
           (production - mean(production))/sd(production))
gf_point(export ~ price, data = Indices)
gf_point(export ~ production, data = Indices)
summary(lm(export  ~ price + production, data = Indices))
```

What if we do it with log  proportional change ...
```{r}
Deltas  <- with(Wheat_export,
  
  data.frame(delta_export = diff(log(export)),
         delta_price = diff(log(price)),
         delta_production = diff(log(production))
  )
)
cor(delta_export ~ delta_price, data = Deltas)
cor(delta_export ~ delta_production, data = Deltas)
gf_point(delta_export ~ delta_price, data = Deltas)
gf_point(delta_export ~ delta_production, data = Deltas)
summary(lm(delta_export ~ delta_price + delta_production, data = Deltas))
```