```
res <-manova(cbind(Sepal.Length, Sepal.Width) ~ Species, data=iris)
summary(res)
```

When running the above code, the result will be as follows:

```
Df Pillai approx F num Df den Df Pr(>F)
Species 2 0.94531 65.878 4 294 < 2.2e-16 ***
Residuals 147
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
```

Now I'm confused by the result of "num Df" and "den Df".

As iris has only 150 rows of data, I thought the sum of dfs should be 149.

However, the value of "den Df" exceeds that and the sums of them seems twice the value.

Then, what do those values mean and what is the relation between them and the "Df" in the leftmost column?

Which values shold I have to report in a paper?

Any help will be appreciated!