An article in the Journal of Sound and Vibration described a study investigating

Question

An article in the Journal of Sound and Vibration described a study investigating the relationship between noise exposure and hypertension. The flowing data are representative of those reported in the article. (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? (b) Fit the simple linear regression model using least squares. Find an estimate of sigma^2. (c) Find the mean rise in blood pressure level associated with a sound pressure level of 85 decibels. (d) Compute a 99% confidence interval on this mean response. (e) Compute a 99% prediction interval on a future observation when the sound pressure level is 85 decibels. (f) What do you notice about the relative size of these two intervals? Which is wider and why?

Explanation / Answer

d)

The 95% confidence interval of mean is  (292.85, 565.65)

e) The 95% prediction interval of new point is (291.56, 566.95

f) The prediction interval is wider than the interval of confidence interval

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