14.27 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/cm 2 on average, with a standard deviation of 95 mg/cm 2 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 predictor variable into a z score.

b. Calculate the predicted z score for the outcome variable.

c. Transform the z score for the outcome variable back into a raw score.

d. Calculate the intercept,

a. e. Calculate the slope,

b. f. Write the equation for the line. g. Draw the line on an empty scatterplot, basing the line on predicted Y values for X values of 0, 1, and 48.