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test H0: 1 0. Minitab performs this test. The P-value is 0.04, indicating that temperature has a signi cant effect on the probability of O-ring failure. The odds ratio is 0.84, so every one degree increase in temperature reduces the odds of failure by 0.84. Figure S11-9 shows the tted logistic regression model. The sharp increase in the probability of O-ring failure is very evident in this graph. The actual temperature at the Challenger launch was 31 F . This is well outside the range of other launch temperatures, so our logistic regression model is not likely to provide highly accurate predictions at that temperature, but it is clear that a launch at 31 F is almost certainly going to result in O-ring failure. It is interesting to note that all of these data were available prior to launch. However, engineers were unable to effectively analyze the data and use them to provide a convincing argument against launching Challenger to NASA managers. Yet a simple regression analysis of the data would have provided a strong quantitative basis for this argument. This is one of the more dramatic instances that points out why engineers and scientists need a strong background in basic statistical techniques.

form the first line of profile attack. Supplementary systems such as Horn s and Bannatyne s are useful when they add to the information yielded by the IQs and indexes, not when they merely echo the same results.

12-1 MULTIPLE LINEAR REGRESSION MODEL 12-1.1 Introduction 12-1.2 Least Squares Estimation of the Parameters 12-1.3 Matrix Approach to Multiple Linear Regression 12-1.4 Properties of the Least Squares Estimators 12-2 HYPOTHESIS TESTS IN MULTIPLE LINEAR REGRESSION 12-2.1 Test for Significance of Regression 12-2.2 Tests on Individual Regression Coefficients and Subsets of Coefficients 12-2.3 More About the Extra Sum of Squares Method (CD Only) 12-3 CONFIDENCE INTERVALS IN MULTIPLE LINEAR REGRESSION 12-3.1 Confidence Intervals on Individual Regression Coefficients

[IBM]

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The two interpretive approaches are similar. The WAIS-III factor indexes and Bannatyne categories each include two scales that assess, in pure form, the verbal and nonverbal dimensions of intelligence that Wechsler intended to measure when he first developed the WechslerBellevue. The Verbal scale measures a person s ability to understand the spoken word and to respond orally. However, only four of the seven WAIS-III tasks Comprehension plus the three (Information, Similarities, Vocabulary) that comprise the Verbal Comprehension Index assess the essence of verbal intelligence: the ability to comprehend verbalizations, verbally mediate during the problem solving or retrieval process, and express one s thoughts in words. These same four subtests constitute Horn s crystallized intelligence grouping. In Bannatyne s system, only three subtests comprise his Verbal Conceptualization factor (Vocabulary, Comprehension, Similarities), because he legitimately considers Information to be more of a memory and achievement-oriented test than a measure of concept formation.

12-4 PREDICTION OF NEW OBSERVATIONS 12-5 MODEL ADEQUACY CHECKING 12-5.1 Residual Analysis 12-5.2 Influential Observations 12-6 ASPECTS OF MULTIPLE REGRESSION MODELING 12-6.1 Polynomial Regression Models 12-6.2 Categorical Regressors and Indicator Variables 12-6.3 Selection of Variables and Model Building 12-6.4 Multicollinearity 12-6.5 Ridge Regression (CD Only) 12-6.6 Nonlinear Regression Models (CD Only)

After careful study of this chapter, you should be able to do the following: 1. Use multiple regression techniques to build empirical models to engineering and scientific data 2. Understand how the method of least squares extends to fitting multiple regression models

Spatial Ability (Bannatyne also includes Object Assembly), simultaneous processing (Kaufman & Lichtenberger, 1999), and analytic thinking (field dependence/field independence cognitive style; Goodenough & Karp, 1961). Regardless of label, the combination reflects the blend of visual perceptual skills, visual motor coordination, and nonverbal reasoning that Wechsler probably intended to measure when he first sought to elevate nonverbal intelligence to the same exalted plateau as verbal intelligence. The Horn model does not have a nonverbal component, but it does yield a scale with a distinct nonverbal flavor: fluid intelligence. This category intends to measure the kind of learning that is not specifically dependent on schooling and formal training, but one that is acquirable in less structured ways. To some extent, Wechsler considered Performance IQ to measure this type of fluid thinking, but Horn focused more on the process than the content of Wechsler s tasks when assigning them to be fluid or crystallized domains. Consequently, four of the Performance subtests are measures of fluid intelligence, but so are two Verbal tasks, namely Similarities and Arithmetic. Similarities is included in the crystallized grouping as well because of the verbal concepts that must be learned before one can uncover their relationships. Arithmetic is a complex task that is not only included in Horn s fluid grouping, but also in his quantitative reasoning (Gq) category and short-term memory (Gsm).

[IBM2]

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