Question 1 Suppose you are interested in the relationship between weight and age for children between 6 and 12 years old. You are considering the following regression models: weight = Bo + Bage + (1) and weight = Bo + Bage + Byage + (2) a. Suppose we evaluate model (1) (the linear model), and obtained the following: weight = 30.6 + 3.6age For 6-year-olds, what is the marginal weight difference for a one-year difference in age? For 12-year-olds, what is the marginal weight difference for a one-year difference in age? b. Suppose we evaluate model (2) (the model with age?), and obtained the following: weight = 32.4 + 3.2age + 0.025age For 6-year-olds, what is the marginal weight difference for one-year difference in age? For 12-year-olds, what is the marginal weight difference for one-year difference in age? c. When and why would you add the age term into the model? In other words, when and why is model (2) a better model than model (1)? Explain. d. Now, suppose you think boys and girls may have different weight distributions. You are considering the following regression models: weight = Bo + Biage + Bymale + (3) weight = Bo + Biage + Pamale + Baage x male + (4)