https://file.aiquickdraw.com/mathbot/file/1727036286469o8ska8og.jpg

### 1. Scatter Diagram:
The scatter plot above displays the relationship between age and systolic blood pressure. Each point represents an individual from the dataset, showing a positive trend — as age increases, systolic blood pressure tends to increase as well.

### 2. Statistical Technique:
To analyze this data, the **Pearson correlation coefficient** is a suitable statistical technique. This method measures the strength and direction of the linear relationship between two variables (in this case, age and systolic blood pressure). The formula for Pearson's \(r\) is:

\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}}
\]

### 3. Correlation Coefficient:
The calculated **Pearson correlation coefficient \(r = 0.972\)**, which is very close to 1, indicates a **strong positive linear relationship** between age and systolic blood pressure. This means as the age increases, systolic blood pressure tends to increase significantly.

Would you like more details or have any specific questions about this? Here are five related questions you could explore:

1. How can we calculate the regression line (line of best fit) for this data?
2. What would be the predicted systolic blood pressure for a person aged 65 based on this data?
3. How does the interpretation of the correlation coefficient change if \(r\) is negative?
4. What are the limitations of Pearson's correlation coefficient?
5. Can we perform hypothesis testing to determine if the correlation is statistically significant?

**Tip:** A correlation close to 1 or -1 does not imply causation, only that there is a strong relationship between the variables.

The following data are taken from a sample of 18 adult females:
Age (X) and Systolic BP (Y) for 18 individuals are provided. The questions are:
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?

Analyze the relationship between age and systolic blood pressure using a scatter plot and calculate the Pearson correlation coefficient. This case study covers statistical techniques for determining the strength and direction of relationships in data.

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