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180 PART II INDIVIDUAL DIFFERENCES ON AGE, SOCIOECONOMIC STATUS, AND OTHER KEY VARIABLES scores for the three oldest cohorts Schaie s data were uncorrected for time-lag and cohort effects, but these adjustments to his data invariably reduce declines, not increase them The comparisons between Wechsler and PMA longitudinal data suggest that (1) the same striking differential V-IQ/P-IQ pattern observed on the Wechsler is not observed for the PMA tasks, and an opposite pattern may prevail for the PMA; (2) the large, early decline in P-IQ does not occur for the PMA, although an earlier verbal decline is evidenced; and (3) if Schaie had used a Wechsler adult scale instead of the PMA in his research, it is unlikely, regardless of his adjustments to the data, that P-IQ would have maintained itself into the 50s or 60s before declining substantially.

11-76. Consider the simple linear regression model 2 Y , with E( ) 0, V( ) , and the 0 1x errors uncorrelated. (a) Show that cov 1 0, 1 2 x 2 Sx x. 2 (b) Show that cov 1Y, 1 0. 11-77. Consider the simple linear regression model 2 Y , with E( ) 0, V( ) , and the 0 1x errors uncorrelated. 2 (a) Show that E( 2 ) E(MSE) . 2 2 (b) Show that E(MSR) 1 Sx x. 11-78. Suppose that we have assumed the straight-line regression model Y

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The reasons for the difference in the relationships of age to P-IQ and the PMA nonverbal tests may relate to the visual motor components of Wechsler s tasks and the cognitive complexity that defines virtually each Performance subtest This complexity makes Wechsler s nonverbal subtests very sensitive to brain damage and psychiatric disorders (see s 8 and 9), as well as aging, and adds to the clinical richness of the scales berger, 1997; Baltes & Mayer, 1999), create a clear picture of aging and cognition Adults performance on tests of crystallized ability (Horn) or pragmatics (Baltes) is maintained during much of the life span and does not decline appreciably until the mid-70s or 80s; in contrast, their performance on tests of fluid visualization speed abilities (Horn) or mechanics (Baltes) declines early in the life span and continues the steady descent throughout middle and old age.

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[Fer75] E. B. Fernandez, R. C. Summers, T. Lang: Definition and Evaluation of Access Rules in Data Management Systems, in Proceedings of the 1st International Conference on Very Large Databases, Boston, 1975, pp. 268 285 E. B. Fernandez, M. M. Larrondo-Petrie, E. Gudes: A Method-Based Authorization Model for Object-Oriented Databases, in Proceedings of the OOPSLA 1993 Workshop on Security in Object-Oriented Systems, pp. 70 79 E. B. Fernandez, J. Wu, M. H. Fernandez: User Group Structures in ObjectOriented Databases, in Proceedings of the 8th Annual IFIP W.G.11.3 Working Conference on Database Security, Bad Salzdetfurth, Germany, August 1994 R. Flanders, E. B. Fernandez: Data Filter Architecture Pattern, in Proceedings of PLoP, 1999 J. Franks, P. Hallam-Baker, J. Hostetler. S. Lawrence. P. Leach, A. Luotonen, L. Stewart: HTTP Authentication: Basic and Digest Access Authentication, RFC 2617, June 1999 E. B. Fernandez, J.C. Hawkins: Determining Role Rights from Use Cases, in Proceedings of the ACM Workshop on Role-Based Access Control, pp. 121 125, 1997 National Institute of Standards and Technology (NIST): Standard for Password Usage, Federal Information Processing Standards Publication 112, Gaithersburg, MD, 1985 D. Firesmith: OPEN Process Framework (OPF) Authentication Requirements, OPEN Process Framework Repository Organization, 2003

where the wi are constants, often called weights. Show that for an objective function in whole each squared residual is multiplied by the reciprocal of the variance of the corresponding observation, the resulting weighted least squares normal equations are

On the WAIS-III, this dichotomy is depicted by the maintenance of V-IQ and VCI and the vulnerability of P-IQ, POI, and PSI The Horn and Baltes theoretical explanations of the classic aging pattern stand in opposition to Botwinick s (1977) speeded unspeeded rationale for the tasks that decline with normal aging versus those that are maintained throughout most of the adult life span In this section we examine the evidence for these competing hypotheses, especially to evaluate whether the agerelated decline on Wechsler s P-IQ, KAIT s Fluid IQ, and on other similar tasks is primarily a function of diminished cognitive capacity or of diminished speed Numerous investigators have interpreted the classical pattern from Botwinick s perspective, for example, Jarvik and Bank (1983) in their longitudinal analysis of aging among elderly twins Indeed, the decline in speed with advancing age is a fact.

but the response is affected by a second variable x2 such that the true regression function is E1Y 2

This slowing is not only an acknowledged laboratory result but also of considerable practical importance... [A]ge-related slowness is evident in tasks of daily living such as zipping a garment, dialing a telephone, picking up coins, unwrapping a band-aid, cutting with a knife, and even putting on a shirt (Salthouse, 1985, p 400) It is also evident from the WAISIII cross-sectional data that the tests that depend the most on visual motor speed, the ones that comprise the PSI, show declines with aging that are steeper than the declines for vulnerable subtests that are less speed-dependent (see, for example, Figure 56) However, the bulk of evidence supports a decline in ability, not just a more generalized difficulty with timed tasks..

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