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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Gas Guzzlers. Use the data on the WeissStats site for gas mileage and engine displacement for 121 vehicles referred to in Exercise 14.41.
To find and interpret a confidence interval, at the specified confidence level for the slope of the population regression line that relates the response variables to the predictor variable.
we repeat the data and provide the sample regression equations for Exercises a.Determine the standard error of the estimate.
b. Construct a residual plot.
c. Construct a normal probability plot of the residuals.
In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts .
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a Te confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).
14.100 Movie Grosses. The data from Exercise 14.36 on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. Specified value of the predictor variable: S 100 million.
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 .
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