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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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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.
Suppose that x and y are predictor and response variables, respectively, of a population. Consider the population that consists of all members of the original population that have a specified value of the predictor variable. The distribution, mean, and standard deviation of the response variable for this population are called the______, ______ and _____ respectively, corresponding to the specified value of the predictor variable.
In Exexcises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b) - (h).
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 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 obfained in part (e).
14.102 Home Size and Value. The data from Exercise 14.38 for home size (in square feet) and assessed value (in thousands of dollars) for the same homes as in Exercise are on the WeissStats site. Specified value of the predictor variable: sq. ft.
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 standand error of the estimate.
b. Construct a residual plot.
c. Construct a normal probability plot of the residuals.
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