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. y 1 0 1 2 5 1 4 6 2 3 x 60 63 65 70 70 70 80 90 80 80 y 5 4 6 8 4 5 7 9 7 6 x 85 89 90 90 90 90 94 100 100 100

(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

Regression resutls are as follows:

Model Summary

S R-sq R-sq(adj) R-sq(pred)
1.31796 74.83% 73.43% 69.21%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -10.13 1.99 -5.08 0.000
Sound Pressure 0.1743 0.0238 7.31 0.000 1.00

Regression Equation

Vibration = -10.13 + 0.1743 Sound Pressure

Part-d

From following output 99^ confidence itnerval on mean response=(3.82184, 5.54506)

Part-e

99% prediction interval on future response=(0.793156, 8.57374)

Paert-f

Prediction interval is wider as for individual observation there is more error than mean of observations.

Prediction for Vibration

Regression Equation

Vibration = -10.13 + 0.1743 Sound Pressure

Variable Setting
Sound Pressure 85

Fit SE Fit 99% CI 99% PI
4.68345 0.299332 (3.82184, 5.54506) (0.793156, 8.57374)

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