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(b) Use the t-test to evaluate the contribution of each regressor to the model. Does it seem that all regressors are necessary Use 0.05. (c) Fit a regression model relating the number of games won to the number of points scored and the number of power

G. I. Seffers: How Biometrics Works, Federal Computer Week, April 30, 2001

Integration/Storage Cognition Evaluation Figural cognition Figural evaluation Fluid ability Holistic (right-brain) processing Nonverbal reasoning Reasoning Simultaneous processing Spatial Spatial relations (CHC) Synthesis Trial-and-error learning Visual processing

play goals. Does this seem to be a logical choice of regressors, considering your answer to part (b) Test this new model for significance of regression and evaluate the contribution of each regressor to the model using the t-test. Use 0.05.

Influences Affecting Scores Ability to respond when uncertain Cognitive style (field dependence) Flexibility Persistence Visual perceptual problems Work under time pressure

12-3 CONFIDENCE INTERVALS IN MULTIPLE LINEAR REGRESSION 12-3.1 Confidence Intervals on Individual Regression Coefficients

[SEI2004]

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In multiple regression models, it is often useful to construct confidence interval estimates for the regression coefficients 5 j 6. The development of a procedure for obtaining these confidence intervals requires that the errors 5 i 6 are normally and independently distributed with mean zero and variance 2. This is the same assumption required in hypothesis testing. Therefore, the observations {Yi} are normally and independently distributed with mean 0 k g j 1 j xij and variance 2. Since the least squares estimator is a linear combination of the observations, it follows that is normally distributed with mean vector and covariance matrix 2 1X X2 1. Then each of the statistics T 2 Cjj

WAIS-III Shared Abilities Worksheet for PICTURE ARRANGEMENT Verbal Subtests Performance Subtests D LN PC Cd PA BD OA SS MR I S A V C

(12-33)

Input Complex verbal directions Distinguishing essential from nonessential detail Visual motor channel Visual perception of complete meaningful stimuli Visual perception of meaningful stimuli

Software Engineering Institute: e-Authentication Risk and Requirements Assessment: e-RA Tool Activity Guide, Pittsburgh, PA, USA, May 2004

has a t distribution with n p degrees of freedom, where Cjj is the jjth element of the 1X X2 1 matrix, and 2 is the estimate of the error variance, obtained from Equation 12-16. This leads to the following 100(1 )% confidence interval for the regression coefficient , j 0, 1, p , k. j Definition

A 100(1 ) % confidence interval on the regression coefficient j, j k in the multiple linear regression model is given by

Integration/Storage Common sensv Convergent-production Crystallized ability Evaluation Fluid ability Integrated brain function Nonverbal reasoning Planning ability Reasoning Semantic content Social comprehension Synthesis Visual sequencing Visualization (CHC)

0, 1, p ,

[SF02] [Sha02]

WAIS-III Shared Abilities Worksheet for PICTURE COMPLETION Verbal Subtests Performance Subtests D LN SS BD OA PC Cd PA MR I S A V C

Because 2 2Cjj is the standard error of the regression coefficient j, we would also write the CI formula as j t 2,n p se1 j 2 t 2,n p se1 j 2. j j t

Input Attention concentration Distinguishing essential from nonessential detail Simple verbal directions Visual motor channel Visual perception of complete meaningful stimuli Visual perception of meaningful stimuli

(12-34)

M. Schumacher, E. B. Fernandez: Focus Group Report: Thinking about Security Patterns, in Proceedings of EuroPLoP, 2002 J. S. Shapiro, N. Hardy: EROS: A Principle-Driven Operating System from the Ground Up, IEEE Software, pp. 26 33, January/February 2002 See also http://www.eros-os.org

EXAMPLE 12-6

Integration/Storage Cognition Evaluation Figural cognition Figural evaluation Holistic (right-brain) processing Simultaneous processing Spatial Visual memory Visual processing

We will construct a 95% confidence interval on the parameter 1 in the wire bond pull strength problem. The point estimate of 1 is 1 2.74427 and the diagonal element of 1X X2 1 corresponding to 1 is C11 0.001671. The estimate of 2 is 2 5.2352, and t0.025,22 2.074. Therefore, the 95% CI on 1 is computed from Equation 12-34 as 2.74427 12.0742 215.235221.0016712

[Sil03] [SFO03] A. Silberschatz, P. Galvin, G. Gagne: Operating System Concepts, Sixth Edition, John Wiley & Sons, 2003 G. Sindre, D. G. Firesmith, A. L. Opdahl: A Reuse-Based Approach to Determining Security Requirements, in Proceedings 9th International Workshop on Requirements Engineering: Foundation for Software Quality (REFSQ 03), Klagenfurt/Velden, Austria, June 2003 R. E. Smith: Authentication: From Passwords to Public Keys, AddisonWesley Professional, 2001 C. Steel, R. Nagappan, R. Lai: Core Security Patterns: Best Practices and Strategies for J2EE, Web Services and Identity Management, Prentice Hall, to be published in 2005

Influences Affecting Scores Work under time pressure Ability to respond when uncertain Alertness to environment Cognitive style (field dependence) Concentration Negativism

12.0742 215.23522 1.0016712

438 12-3.2

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