Let's assume we know that age is related to bone density, with a Pearson correlation coefficient of 0.19. (Notice that the correlation is negative, indicating that bone density tends to be lower at older ages than at younger ages.) Assume we also know the following descriptive statistics:
Age of people studied: 55 years on average, with a standard deviation of 12 years.
Bone density of people studied: 1000 mg/cm2 on average, with a standard deviation of 95 mg/cm.
Virginia is 76 years old. What would you predict her bone density to be? To answer this question, complete the following steps:
a. Transform the raw score for the independent variable to a z score.
b. Calculate the predicted z score for the dependent variable.
c. Transform the z score for the dependent variable back into a raw score.