Question 1

A. Draw a scatter diagram of y (blood pressure rise in millimeters of mercury) versus x (sound pressure level in decibels). Does a simple linear regression model seem reasonable in this situation?

Yes, because the dependent variable y has a visible linear relationship with the independent variable x in the scattered diagram.

Scattered Diagram

B. Fit the simple linear regression model using least squares. Find an estimate of σ^2.

y = 0.17x - 10.13

The estimated σ^2 is 28.06316. 

The Linear Regression Model

C. Find the predicted mean rise in blood pressure level associated with a sound pressure level of 85 decibels.

Using the

with β(0) = -10.13 and β(1) = 0.17429

The predicted mean rise in y, blood pressure level, with x, sound pressure level, 85 is 4.68311 ≈ 5.