It is commonly expected that as a person ages, their muscle mass decreases. To further examine this relationship in women, a nutritionist randomly selected 60 female patients from her clinic, 15 women from each 10-year age group beginning with age 40 and ending with age 80. For each patient, her age and current muscle mass was recorded. A scatterplot, least squares regression line, and coefficient of determination are as follows.
-Which of the following is a correct interpretation of the coefficient of determination?
A) When the age of a woman is equal to zero, her predicted muscle mass is 75.01 lbs.
B) The correlation coefficient between age and muscle mass is equal to 0.7501.
C) Each additional year in age is associated with a 75.01% decrease in predicted muscle mass.
D) Approximately 75.01% of the variation in muscle mass can be explained by changes in age among these women.

Question

It is commonly expected that as a person ages, their muscle mass decreases. To further examine this relationship in women, a nutritionist randomly selected 60 female patients from her clinic, 15 women from each 10-year age group beginning with age 40 and ending with age 80. For each patient, her age and current muscle mass was recorded. A scatterplot, least squares regression line, and coefficient of determination are as follows. 
-Which of the following is a correct interpretation of the coefficient of determination?
A) When the age of a woman is equal to zero, her predicted muscle mass is 75.01 lbs. 
B) The correlation coefficient between age and muscle mass is equal to 0.7501. 
C) Each additional year in age is associated with a 75.01% decrease in predicted muscle mass. 
D) Approximately 75.01% of the variation in muscle mass can be explained by changes in age among these women.

Quizplus · Accepted Answer

The coefficient of determination, often denoted as R², represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). In this context, it means that 75.01% of the variation in muscle mass can be explained by age.

It Is Commonly Expected That as a Person Ages, Their