Calculating the covariance

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**Covariance as the mean of cross products**

Before breaking this down, I show the whole game: `\(\Sigma{(X_i-\overline{X})(Y_i-\overline{Y})}/(n-1)\)`

``` r
gc_rils                                                             |>
    filter(!is.na(log10_petal_area_mm), !is.na(prop_hybrid))        |>
    mutate(dev_x = log10_petal_area_mm - mean(log10_petal_area_mm)) |>
    mutate(dev_y       = prop_hybrid - mean(prop_hybrid))           |>
    mutate(cross_prod  = dev_x* dev_y)                              |>
    summarise(sumXprod = sum(cross_prod),
              n        = n(),
              covar    = sumXprod/ (n-1))
```

| sumXprod|  n|  covar|
|--------:|--:|------:|
|   0.7413| 99| 0.0076|

---

# Let's work through this!

---

**Find means**

``` r
gc_rils                                                     |>
  filter(!is.na(log10_petal_area_mm),  !is.na(prop_hybrid))|>
  select(x      = log10_petal_area_mm, y = prop_hybrid )   |>
  mutate(mean_x = mean(x))                                 |>
  mutate(mean_x = mean(y)) 
```

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---

**Find deviations**

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---

**Find cross products**

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---

**Summing cross products**

| sum_cross_prod|
|--------------:|
|         0.7413|

---

**Dividing by  `\((n - 1)\)`**

| sum_cross_prod|  covar|
|--------------:|------:|
|         0.7413| 0.0076|

---

# *'Fin'*