Exercise

# Modeling an interaction

In this exercise you will use interactions to model the effect of gender and gastric activity on alcohol metabolism.

The data frame `alcohol`

has columns:

`Metabol`

: the alcohol metabolism rate`Gastric`

: the rate of gastric alcohol dehydrogenase activity`Sex`

: the sex of the drinker (`Male`

or`Female`

)

In the video, we fit three models to the `alcohol`

data:

- one with only additive (main effect) terms :
`Metabol ~ Gastric + Sex`

- two models, each with interactions between gastric activity and sex

We saw that one of the models with interaction terms had a better R-squared than the additive model, suggesting that using interaction terms gives a better fit. In this exercise we will compare the R-squared of one of the interaction models to the main-effects-only model.

Recall that the operator `:`

designates the interaction between two variables. The operator `*`

designates the interaction between the two variables, plus the main effects.

```
x*y = x + y + x:y
```

Instructions

**100 XP**

The data frame `alcohol`

is in your workspace.

- Write a formula that expresses
`Metabol`

as a function of`Gastric`

and`Sex`

with no interactions.- Assign the formula to the variable
`fmla_add`

and print it.

- Assign the formula to the variable
- Write a formula that expresses
`Metabol`

as a function of the interaction between`Gastric`

and`Sex`

.- Add
`Gastric`

as a main effect, but not`Sex`

. - Assign the formula to the variable
`fmla_interaction`

and print it.

- Add
- Fit a linear model with only main effects:
`model_add`

to the data. - Fit a linear model with the interaction:
`model_interaction`

to the data. - Call
`summary()`

on both models. Which has a better R-squared?