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I. Welch: Reflective Enforcement of the Clark-Wilson Integrity Model, in Proceedings of the 2nd Workshop in Distributed Object Security, pp. 5 9, OOPSLA 1999, November 1999 C. Wood, E. B. Fernandez: Authorization in a Decentralized Database System, in Proceedings of the 5th International Conference on Very Large Databases, pp. 352 359, Rio de Janeiro, 1979 B. Woolf: The Null Object Pattern, in [PLoPD3], Addison-Wesley, 1997 J. Whittaker, H. H. Thompson: How to Break Software Security, AddisonWesley, 2003 J. Wack, M. Tracy, M. Souppaya: Guideline on Network Security Testing, NIST Special Publication 800-42, National Institute of Standards and Technology (NIST), 2003 Yahoo Security Directory

x0 2

Verbal Subtests I S A V C D LN PC Cd PA Performance Subtests BD OA SS + MR S or W

(12-40)

http://dir.yahoo.com/Computers_and_Internet/ Security_and_Encryption/

Input Complex verbal directions Visual perception of abstract stimuli Visual motor channel + + o o

This prediction interval is a generalization of the prediction interval given in Equation 11-33 for a future observation in simple linear regression. If you compare the prediction interval Equation 12-40 with the expression for the confidence interval on the mean, Equation 12-38, you will observe that the prediction interval is always wider than the confidence interval. The confidence interval expresses the error in estimating the mean of a distribution, while the prediction interval expresses the error in predicting a future observation from the distribution at

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the point x0. This must include the error in estimating the mean at that point, as well as the inherent variability in the random variable Y at the same value x x0. In predicting new observations and in estimating the mean response at a given point x01, x02, . . . , x0k, we must be careful about extrapolating beyond the region containing the original observations. It is very possible that a model that fits well in the region of the original data will no longer fit well outside of that region. In multiple regression it is often easy to inadvertently extrapolate, since the levels of the variables (xi1, xi2, . . . , xik), i 1, 2, . . . , n, jointly define the region containing the data. As an example, consider Fig. 12-5, which illustrates the region containing the observations for a two-variable regression model. Note that the point (x01, x02) lies within the ranges of both regressor variables x1 and x2, but it is outside the region that is actually spanned by the original observations. Thus, either predicting the value of a new observation or estimating the mean response at this point is an extrapolation of the original regression model. EXAMPLE 12-8 Suppose that the engineer in Example 12-1 wishes to construct a 95% prediction interval on the wire bond pull strength when the wire length is x1 8 and the die height is x2 275. Note 27.66. that x [1 8 275], and the point estimate of the pull strength is y0 x 0 0 Also, in Example 12-7 we calculated x 1 2 1x0 0.04444. Therefore, from Equation 0 12-40 we have 27.66 2.074 25.235211

Integration/Storage Cognition Concept formation Evaluation Figural cognition Figural evaluation Fluid ability General ability

[Woo79]

2.074 25.235211

Picture Completion; Cd = Digital Symbol-Coding; PA = Picture Arrangement; BD = Block Design; OA = Object Assembly; SS = Symbol Search; MR = Matrix Reasoning.

Notice that the prediction interval is wider than the confidence interval on the mean response at the same point, calculated in Example 12-7. The Minitab output in Table 12-4 also displays this prediction interval.

NOTE: See Ryan N s score profile on p. 452 for details on how +, , and 0s were determined. I = Information; S = Similarities; A = Arithmetic; V = Vocabulary; C = Comprehension; DS = Digit Span; LN = Letter-Number Sequencing; PC =

EXERCISES FOR SECTIONS 12-3 AND 12-4

[Woolf96] [WT03] [WTS03]

12-26 Consider the soil absorption data in Exercise 12-2 (a) Find a 95% confidence interval on the regression coefficient 1 (b) Find a 95% confidence interval on mean soil absorption index when x1 200 and x2 50 (c) Find a 95% prediction interval on the soil absorption index when x1 200 and x2 50 12-27 Consider the NFL data in Exercise 12-4 (a) Find a 95% confidence interval on 8 (b) What is the estimated standard error of Y |x0 when x2 2000 yards, x7 60%, and x8 1800 yards (c) Find a 95% confidence interval on the mean number of games won when x2 2000, x7 60, and x8 1800 12-28 Consider the gasoline mileage data in Exercise 12-5 (a) Find 99% confidence intervals on 1 and 6 (b) Find a 99% confidence interval on the mean of Y when x1 300 and x6 4.

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