abstract In this paper we introduce certain numbers, called collinearity indices, which are useful in detecting near collinearities in regression problems. The coeecients enter adversely into formulas concerning signiicance testing and the eeects of errors in the regression variables. Thus they provide simple regression diagnostics, suitable for incorporation in regression packages.

We revisit compressed least squares (CLS) regression as originally analyzed in Maillard and Munos (2009) and later on in Kaban (2014) with some refinements. Given a set of high-dimensional inputs, CLS applies a random projection and then performs least squares regression based on the projected inputs of lower dimension. This approach can be beneficial with regard to both computation (yielding a...

Number of latents The same number of factors will be extracted for PLS responses as for PLS factors. The researcher must specify how many latents to extract (in SPSS the default is 5). There is no one criterion for deciding how many latents to employ. Common alternatives are: 1. Cross-validating the model with increasing numbers of factors, then choosing the number with minimum prediction error...

Lunate and perilunate dislocations are uncommon, but they have clinical importance because complications, such as median neuropathy and avascular necrosis of the lunate, can occur. Although early diagnosis enabling early surgical treatment is crucial for preventing long-term sequelae, these dislocations are frequently missed in the initial assessment. Imaging tools, such as plain radiography, m...

Introduction: The shapes produced on terrestrial surfaces that are continually subject to aeolian processes range in size from tiny ripples to giant draa [1]. The physical mechanism of the formation of ripples, the smallest of aeolian bedforms, is intimately related to saltation and reptation processes. Sand and granule ripples are typically tens of reptation path lengths wide and do not alter ...

Dunes are present in nearly all fluvial channels and are vital in understanding sediment transport, deposition, and flow conditions during floods of rivers and estuaries. This information is pertinent for helping developing management practices to reduce risks in river transportation and engineering. Although a few recent studies have investigated the micromorphology of a portion of the Yangtze...