Final answer:
Dr. Carson can use a factorial design to study the impact of exercise regimes A, B, and C on weight change in obese adolescents, while also considering the age of the teenagers as an additional factor.
Step-by-step explanation:
Dr. Carson can design the study by including exercise regimes A, B, and C as the main independent variable and age as an additional independent variable. To incorporate both variables, she can use a factorial design, where each combination of exercise regime and age is tested.
For example, she can have three groups: Group 1 doing regime A with teenagers aged 13-15, Group 2 doing regime B with teenagers aged 13-15, and Group 3 doing regime C with teenagers aged 13-15.
Then, she can repeat the same groups but with teenagers aged 16-18. This design allows Dr. Carson to analyze the main effects of exercise regimes and age, as well as any potential interactions between them.