A weight loss company wanted to predict how much weight a client would lose if they followed a prescribed exercise program in addition to the company's diet program. Volunteers were randomly divided into two groups, one group dieted but didn't exercise, and the other group dieted and followed the exercise program. For the exercise group, they used linear regression with percent compliance with the exercise program as the explanatory variable and pounds lost in three months as the response variable. One of the clients was told that his residual was 5.5 pounds. What does this mean?

Options:

a. His predicted weight loss was 5.5 pounds higher than his actual weight loss.

b. His actual weight loss was 5.5 pounds higher than his predicted weight loss.

c. His actual weight loss was 5.5 pounds higher than it would have been if he didn't exercise.

d. His predicted weight loss was 5.5 pounds higher than it would have been if he didn't exercise.

Answer:

Option B. His actual weight loss was 5.5 pounds higher than his predicted weight loss.

Step-by-step explanation:

In regression analysis, the difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e). Residual value = Observed value - Predicted value. i. e. e = y - ŷ

Since the residual weight of the client was 5.5 pounds, this means that His actual weight after compliance with the exercise program his 5.5 pounds higher than what he predicted.