Writing formulas for GAM models (2)

Suppose that in the diet problem from the previous exercise, you now also want to take into account

• the dieter's resting metabolic rate (BMR -- continuous) and
• the dieter's average number hours of aerobic exercise per day (E -- continuous) at the beginning of the study.

You have reason to believe that the relationship between BMR and weight loss is linear (and you want to model it that way), but not necessarily the relationship between aerobic exercise and weight loss.

Which is the most appropriate formula?