The equation of the least squares regression line is:

$\hat{y} = 0.908x + 100.28$

Where:

• $x$ is the age of the individual.
• $y$ is the predicted systolic blood pressure.

For individual 22, who is 50 years old:

• The predicted systolic blood pressure is approximately 145.66 mm Hg.
• The actual systolic blood pressure is 142 mm Hg.

The residual for individual 22 is:

$\text{Residual} = \text{Actual value} - \text{Predicted value} = 142 - 145.66 = -3.66 \, \text{mm Hg}$

Interpretation:

• The actual systolic blood pressure is below the predicted value by about 3.66 mm Hg.
• The residual tells us that individual 22's systolic blood pressure is slightly lower than expected based on their age.

Would you like more details or explanations? Here are some related questions for practice:

1. How do we interpret the slope of the regression line in this context?
2. What would the predicted blood pressure be for someone aged 60?
3. Can you calculate the residual for another individual, say individual 10?
4. What does a positive residual indicate in this context?
5. How can we assess the accuracy of the regression model?

Tip: Residuals can tell us how well the regression model fits individual data points — the closer to zero, the better the fit for that individual.