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whereas the standard deviation of ~LAD is approximately T / VL( Xi - i)2 (the approximation is better for large sample sizes). Thus the ratio T /(T determines which of the two regression methods is better for estimating the slope of the regression line. Both T and (T are measures of the size of the random errors. T is equal to 1/(28), where 8 is the probability density of the error distribution at its median. (When doing LAD regression, the assumption is sometimes made that the median, rather than the mean, of the error distribution is O. If the error distribution is symmetric, its mean and median coincide.) If (T is large, then the errors are widely spread out, so the probability density near the median is low, hence 8 is small, which implies T is large. So, roughly speaking, T is large when (T is large and T is small when (T is small. But the exact ratio T / (T depends on the shape of the distribution of the population of errors. If the errors have a normal distribution, then T / (T = 1.253 > 1, and so, at least for large sample sizes, the LAD regression estimates are less accurate then the least-squares regression estimates. If the errors have a Laplace distribution, then T / (T = 0.707 < 1. Justification of (4.5). Our justification assumes a large sample size n. Then m is approximately equal to n and the residuals i behave much the same as the true errors ei We will argue that T can be approximated by

With the release of Windows 3.0 came the introduction of the toolbar (which we discuss at length in 23), an idiom that has grown into a de facto standard as familiar as the menu bar. To populate the toolbar, the button was adapted from its traditional home on the dialog box. On its way, it expanded significantly in function, role, and visual aspect. On dialog boxes, the button is rectangular (with rounded edges on the Mac) and exclusively labeled with text. When it moved to the toolbar, it became square, lost its text, and acquired a pictograph, an iconic legend. Thus was born the butcon: half button, half icon (see Figure 21-2). In Windows 98, the butcon, or toolbar button, continued to develop, losing its raised affordance except when used a move to reduce visual clutter in response to the overcrowding of toolbars. Unfortunately, this makes it more difficult for newcomers to understand the idiom; starting with Windows 2000, the toolbar butcon now reveals its button affordance only when pointed at.

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horizontal shear, are the three qualities that are normally determined during the process of selection we call design Because timber is available in certain standard lumber sizes, the designer selects from those available, the size, grade, and species that most economically meets the preordained standards for bending stress, de ection, and horizontal shear When the engineer reviews the capacity of an existing member, many parameters complicate this process Size, span, and spacing of members are dictated by the existing structure It is the engineer s task to determine the size, orientation, species, grade, and end condition of all the structural elements in a building that already exists The freedom of choice afforded by design is therefore reduced in the review process Often, the structural engineer must pass judgment on a structure that has served far beyond what we consider to be a normal period of service.

vn[C(k 2 ) - c(k,)l/4 where kl and k2 are the closest integers to (n + 1)/ 2 vn. Our argument consists of deriving two approximate 95%-confidence intervals for the median of the error distribution, both based on normal approximations, and equating their lengths. Recall from the preceding subsection that T in LAD regression is analogous to (T in least-squares regression. The standard deviation of an LS regression estimate has the form (TC, whereas the standard deviation of the corresponding LAD regression estimate is approximately TC for the same quantity c. In particular, consider the special case of "regression" when p = 0, that is, when there are no explanatory variables and we simply have a random sample of n independent observations from the same population, such as e 1, e 2 , , ell. The LS "regression" estimate is the sample mean e, because a = e is the value of a that gives the least sum of squared deviations Dei - a)2. Its standard deviation is (T / vn. The LAD "regression" estimate is the sample median e, because a = e is the value of a that gives the least sum of absolute deviations Lie, - al. Its standard deviation is approximately T/vn.

Figure 21-2 Butcons from Microsoft Office 2003. On the left are examples in Office for Windows, and on the right are the same examples in Office for OS X. Notice how each item isn t rendered as a distinct button until the mouse cursor passes over it.

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