Question

Let’s say that, generally speaking, Amy thinks exercise is good for your health, but if you exercise for more than four hours per day, every day, exercise begins harming your health. Amy runs the following regression. Exercise is in hours of exercise per week. Does the following equation support Amy’s belief? Please explain.

Health = 6 + 30Exercise – 12Exercise2.

In case, the squared term doesn't appear correctly in some people's browsers, I have written the above formula a slightly different way below.

Health = 6 + 30Exercise – 12Exercise^2.

Answer 1

We have to notice here that there is a positive relationship between exercise and health. But there is a negative relationship between the squared term of exercise and health. This means that as the exercise time increases the squared term would impact health negatively.

For example:

Let us say your exercise for two hours per day.

Health = 6 + 30*2 – 12*2².

Health = 18

Let us say your friend exercise for five hours per day.

Health = 6 + 30*5 – 12*5².

Health = -144

Thus, it is clear that as the exercise time increases, health is harmed.

Therefore, we can support Amy’s belief.