To find the least-squares regression line equation $\hat{y} = a + bx$ that predicts the diastolic pressure $y$ from the systolic pressure $x$, we need to calculate:

1. The slope $b$.
2. The y-intercept $a$.

The formulas to compute $a$ and $b$ are as follows:

$b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$ $a = \bar{y} - b\bar{x}$

Where:

• $x_i$ and $y_i$ are the individual values of systolic and diastolic pressures, respectively.
• $\bar{x}$ and $\bar{y}$ are the means of the systolic and diastolic pressures.

Let’s calculate these values using the data provided:

I'll work through these calculations now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you'd like to proceed manually, I can guide you step-by-step through the calculations for finding the slope and intercept. Alternatively, feel free to upload any further details or ask questions.

If you're ready to proceed with more questions, here are some that might extend your understanding of regression analysis:

1. How is the least-squares regression line used to make predictions in real-world scenarios?
2. What does the slope of the regression line represent in the context of blood pressure?
3. How would you interpret the y-intercept in this specific case?
4. What are the assumptions underlying a simple linear regression model?
5. How does the correlation coefficient relate to the strength of this regression?

Tip: When performing regression analysis, always check the correlation to understand the strength and direction of the linear relationship.