We can make the following observations:

1. For the interval given under 95% CI, we say with 95% confidence we can estimate that in hospitals in which the average length of stay is 10 days, the mean infection risk is between 4.25921 and 4.79849.
2. For the interval given under 95% PI, we say with 95% confidence that for any future hospital where the average length of stay is 10 days, the infection risk is between 2.45891 and 6.59878.
3. The value under Fit is calculated as \(\hat{y} = −1.160 + 0.5689(10) = 4.529\).
4. The value under SE Fit is the standard error of \(\hat{y}\) and it measures the accuracy of \(\hat{y}\) as an estimate of E(Y ).
5. Since df = n − 2 = 58 − 2 = 56, the multiplier for 95% confidence is 2.00324. The 95% CI for E(Y) is calculated as \begin{align} &=4.52885 \pm (2.00324 × 0.134602)\\ &= 4.52885 \pm 0.26964\\ &= (4.259, 4.798)\end{align}
6. Since S = \(\sqrt{MSE}\) = 1.02449, the 95% PI is calculated as \begin{align} &=4.52885 \pm (2.00324 × \sqrt{1.02449^2 + 0.134602^2})\\ &= 4.52885 \pm 2.0699 = (2.459, 6.599)\end{align}