Question 1

figure 1.

A.

By using the plot function in R, as well as the simple linear regression line function, we are able to get the following graph:

figure 2.

Cross-checking the simple linear regression line with our equation below, we can confirm that this is indeed correct.

The simple linear regression model seems appropriate for this situation as there is a single regressor, the sound pressure level, and a dependent variable, the blood pressure rise. We can see the relation that as the sound pressure level rises in decibels, the rise in blood pressure increases as well, in millimeters of mercury.

B.

table 1.

We can get the unbiased estimate σ2 by using the following formula:
\[σ^2=\frac{\Sigma (y-\hat{y})^2}{n-2}\]

With the help of table 1. above, the estimate of σ2 is: \[σ^2=\frac{31.27714}{20-2}=1.74\]

C.

From the equation in table 1. above:

\[\hat{y}=-10.13+0.174x\]

we can plug in the value of x with 85 decibels to find the prediced mean rise in blood pressure for this specific value.

\[\hat{y}=-10.13+0.174(85)=4.66\]

At the sound pressure of 85 decibels, we can predict a 4.66 millimeter rise in blood pressure level.