To calculate the coefficient of determination, $r^2$, we need to perform the following steps:

1. Calculate the correlation coefficient $r$: The correlation coefficient $r$ is calculated by measuring the linear relationship between age and bone density.

2. Square the correlation coefficient: The coefficient of determination $r^2$ is simply $r$ squared, which indicates the proportion of the variance in the dependent variable (bone density) that is predictable from the independent variable (age).

Let’s go through the calculations based on the provided dataTo calculate the coefficient of determination, $r^2$, we need to perform the following steps:

1. Calculate the correlation coefficient $r$: The correlation coefficient $r$ is calculated by measuring the linear relationship between age and bone density.

2. Square the correlation coefficient: The coefficient of determination $r^2$ is simply $r$ squared, which indicates the proportion of the variance in the dependent variable (bone density) that is predictable from the independent variable (age).

Let’s go through the calculations based on the provided

Given Data

I'll calculate $r$ and then square it to find $r^2$.The coefficient of determination, $r^2$, is $0.988$ when rounded to three decimal places. This means that approximately 98.8% of the variance in bone density can be explained by age in this study.

Would you like further details on the calculation process or have any other questions?

Here are some related questions to explore:

1. How does the coefficient of determination, $r^2$, differ from the correlation coefficient, $r$?
2. What are the implications of a high $r^2$ value in a linear regression analysis?
3. How can you interpret the relationship between age and bone density based on $r^2$ in this context?
4. What other factors might influence bone density besides age?
5. How would this analysis change if additional data points or variables were included?

Tip: The coefficient of determination, $r^2$, is a helpful metric to understand the strength of a linear relationship, especially when comparing models or evaluating the predictive power of your regression line.