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Suppose you are interested in looking at the relationship between time spent engaging in aerobic exercise or cardio, and weight loss for a group of

Suppose you are interested in looking at the relationship between time spent engaging in aerobic exercise or cardio, and weight loss for a group of people attempting to lose weight over the course of two months. You estimate

weight = 0 + 1 hours + 2 male +

where weight means your weight in pounds after the two-month period. hours means the total number of hours the person got their heart rate above 140 beats per minute during the two month period. Suppose you think there are diminishing returns to aerobic exercise, which model accommodates this possibility? What would be the sign of any new betas in your model?

weight = 0 + 1 hours2 + 2 male + , positive

weight = 0 + 1 hours2 + 2 male + , negative

weight = 0 + 1 hours + 2 hours2 + 3 male + , positive

weight = 0 + 1 hours + 2 hours2 + 3 male + , positive, negative

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