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Here is the scatter plot illustrating the relationship between age (\( X \)) and systolic blood pressure (\( Y \)). From the plot, we observe a generally positive trend, indicating that systolic blood pressure tends to increase with age.

Next, I will calculate the Pearson correlation coefficient to quantify the strength of this relationship.The Pearson correlation coefficient \( r \) between age and systolic blood pressure is approximately **0.768**. This indicates a moderately strong positive linear relationship, suggesting that as age increases, systolic blood pressure tends to rise.

### Interpretation of \( r \):
- Since \( r = 0.768 \), there is a clear positive correlation, meaning older adults in this sample tend to have higher systolic blood pressure.
- However, this value is not close to 1, so the relationship is not perfectly linear, implying other factors might also affect blood pressure.

Would you like to explore further details or have any specific questions?

Here are some follow-up questions:
1. What would the scatter plot look like if the correlation coefficient were negative?
2. How can we calculate the coefficient of determination from the correlation coefficient?
3. What other statistical techniques can we use to analyze the relationship between age and blood pressure?
4. How does the value of \( r \) affect the interpretation of trends in different age groups?
5. What does a correlation of 0 imply in the context of age and blood pressure?

**Tip:** To further explore this relationship, consider performing a regression analysis to predict systolic blood pressure based on age.

The following data are taken from a sample of 18 adult females: age (X) and systolic blood pressure (Y). 1) Draw a scatter diagram to display the relationship between the two variables. 2) Describe the statistical technique you should use to analyze such data and calculate the value. 3) For the correlation coefficient in this case, what is the value of r and its interpretation?

Explore the statistical relationship between age and systolic blood pressure in adult females through scatter plots and Pearson's correlation coefficient. Learn how to calculate and interpret the value of r, indicating the strength and direction of the relationship. Suitable for college-level statistics students.

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