- The variable, age, would be added first, since the single variable model with age has the highest adjusted-\(R^2\), 0.5716, of the three single variable models.
- The second variable added would be sex, since out of the two two variable models with age (1. age and sex 2. age and smoke) the model with age and sex has the higher adjusted-\(R^2\) of 0.6058.
- While the adjusted-\(R^2\) does increase to 0.6075 for the three variable model, the increase is minimal, so a case could be made for both the three variable model and the two variable model with just age and sex.
- Dropping smoke, decreases the BIC from -588.7677 to -591.3395. Dropping the other two variables increases the BIC. This means that we would drop smoke.
- Removing any of the other two remaining variables would lead to an increase in BIC, so we would stop at the two variable model. Again note that, dropping smoke from the three variable model only led to a slight decrease in the BIC, so a case could be made for the three variable model as well.