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Chapter 14: Q 8 (page 588)
Generally speaking, what is the difference between a confidence interval and a prediction interval?
Confidence is usually reserved for interval estimates of the parameters, Prediction is used for interval estimates of variables.
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In Exercises 14.12-14.21, we repeat the data and provide the sample regression equations for Exercises 4.48 -4.57.
a. Determine the standard error of the estimate.
b. Construct a residual plot.
c. Construct a normal probability plot of the residuals.
Crown-Rump Length. In the article "The Human Vomeronasal Organ. Part II: Prenatal Development" (Joumal of Anatomy, Vol. 197, Issue 3, pp. 421-436), T. Smith and K. Bhatnagar examined the controversial issue of the human vomeronasal organ, regarding its structure, function, and identity. The following table shows the age of fetuses , in weeks, and length of crown-rump , in millimeters.
14.95 Plant Emissions. Following are the data on plant weight and quantity of volatile emissions from Exercise 14.25.
| x | 57 | 85 | 57 | 65 | 52 | 67 | 62 | 80 | 77 | 53 | 68 |
| y | 8.0 | 22.0 | 10.5 | 22.5 | 12.0 | 11.5 | 7.5 | 13.0 | 16.5 | 21.0 | 12.0 |
a. Obtain a point estimate for the mean quantity of volatile emissions of all (Solanum tuberosum) plants that weigh .
b. Find a confidence interval for the mean quantity of volatile emissions of all plants that weigh .
c. Find the predicted quantity of volatile emissions for a plant that weighs .
d. Determine a prediction interval for the quantity of volatile emissions for a plant that weighs .
Regarding the standard error of the estimate,
a. give two interpretations of it.
b. identify another name used for it, and explain the rationale for that name.
c. which one of the three sums of squares figures in its computation?
In this Exercise 14.52, we repeat the information from Exercise 14.16.
a. Decide, at the significance level, whether the data provide sufficient evidence to conclude that is useful for predicting :
b. Find a confidence interval for the slope of the population regression line.
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