Assumptions of Multiple Regression: Correcting Two Misconceptions

In 2002, an article entitled Four assumptions of multiple regression that researchers should always test by Osborne and Waters was published in PARE. This article has gone on to be viewed more than 275,000 times.(as of August 2013), and it is one of the first results displayed in a Google search for regression assumptions . While Osborne and Water\u27s efforts in raising awareness of the need to check assumptions.when using regression are laudable, we note that the original article contained at least two fairly important.misconceptions about the assumptions of multiple regression: Firstly, that multiple regression requires the.assumption of normally distributed variables; and secondly, that measurement errors necessarily cause.underestimation of simple regression coefficients. In this article, we clarify that multiple regression models.estimated using ordinary least squares require the assumption of normally distributed errors in order for.trustworthy inferences, at least in small samples, but not the assumption of normally distributed response or.predictor variables. Secondly, we point out that regression coefficients in simple regression models will be.biased (toward zero) estimates of the relationships between variables of interest when measurement error is.uncorrelated across those variables, but that when correlated measurement error is present, regression.coefficients may be either upwardly or downwardly biased. We conclude with a brief corrected summary of.the assumptions of multiple regression when using ordinary least squares. Accessed 36,189 times on https://pareonline.net from September 06, 2013 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Impact of the North Atlantic Oscillation on transatlantic flight routes and clear-air turbulence

The variation of wind-optimal transatlantic flight routes and their turbulence potential is investigated to understand how upper-level winds and large-scale flow patterns can affect the efficiency and safety of long-haul flights. In this study, the wind-optimal routes (WORs) that minimize the total flight time by considering wind variations are modeled for flights between John F. Kennedy International Airport (JFK) in New York, New York, and Heathrow Airport (LHR) in London, United Kingdom, during two distinct winter periods of abnormally high and low phases of North Atlantic Oscillation (NAO) teleconnection patterns. Eastbound WORs approximate the JFK–LHR great circle (GC) route following northerly shifted jets in the +NAO period. Those WORs deviate southward following southerly shifted jets during the −NAO period, because eastbound WORs fly closely to the prevailing westerly jets to maximize tailwinds. Westbound WORs, however, spread meridionally to avoid the jets near the GC in the +NAO period to minimize headwinds. In the −NAO period, westbound WORs are north of the GC because of the southerly shifted jets. Consequently, eastbound WORs are faster but have higher probabilities of encountering clear-air turbulence than westbound ones, because eastbound WORs are close to the jet streams, especially near the cyclonic shear side of the jets in the northern (southern) part of the GC in the +NAO (−NAO) period. This study suggests how predicted teleconnection weather patterns can be used for long-haul strategic flight planning, ultimately contributing to minimizing aviation’s impact on the environmen

Modelling and valuing the environmental impacts of arable, forestry and agroforestry systems: a case study

The use of land for intensive arable production in Europe is associated with a range of externalities that typically impose costs on third parties. The introduction of trees in arable systems can potentially be used to reduce these costs. This paper assesses the profitability and environmental externalities of a silvoarable agroforestry system, and compares this with the profitability and environmental externalities from an arable system and a forestry system. A silvoarable experimental plot of poplar trees planted in 1992 in Bedfordshire, Eastern England, was used as a case study. The Yield-SAFE model was used to simulate the growth and yields of the silvoarable, arable, and forestry land uses along with the associated environmental externalities, including carbon sequestration, greenhouse gas emissions, nitrogen and phosphorus surplus, and soil erosion losses by water. The Farm-SAFE model was then used to quantify the monetary value of these effects. The study assesses both the financial profitability from a farmer perspective and the economic benefit from a societal perspective. The arable option was the most financially profitable system followed by the silvoarable system and forestry. However, when the environmental externalities were included, silvoarable agroforestry provided the greatest benefit. This suggests that the appropriate integration of trees in arable land can provide greater well-being benefits to society overall, than arable farming without trees, or forestry systems on their own

Maximising potential: The psychological effects of the youth development programme Project K

Project K is a positive youth development programme targeting 13-15 year old students with low self-efficacy. It involves three components: wilderness adventure, community challenge and individual mentoring. This longitudinal study aimed to investigate changes in self-efficacy, resilience, connectedness and wellbeing in students participating in Project K. Eighty students (59% male) were recruited from five secondary schools across the North Island of New Zealand for a quasi-experimental study. Participants displaying delinquent behaviour, self-harm, suicidal ideation, or an eating disorder were excluded. Over 14 months, six waves of measurement were completed by Project K participants (n = 49), while four waves of measurement were completed by a control group (n = 31). Analyses using multilevel models showed that completion of Project K had substantial positive effects on self-efficacy, resilience, and wellbeing, although the effect on connectedness was not significant. We conclude that Project K appears to be an effective positive youth development programme for adolescents with low self-efficacy

Network analysis applied to post-concussion symptoms in two mild traumatic brain injury samples

ObjectiveA latent disease explanation cannot exclusively explain post-concussion symptoms after mild traumatic brain injury (mTBI). Network analysis offers an alternative form of explanation for relationships between symptoms. The study aimed to apply network analysis to post-concussion symptoms in two different mTBI cohorts; an acute treatment-seeking sample and a sample 10 years post-mTBI.MethodThe treatment-seeking sample (n = 258) were on average 6 weeks post-injury; the 10 year post mTBI sample (n = 193) was derived from a population-based incidence and outcomes study (BIONIC). Network analysis was completed on post-concussion symptoms measured using the Rivermead Post-Concussion Questionnaire.ResultsIn the treatment-seeking sample, frustration, blurred vision, and concentration difficulties were central to the network. These symptoms remained central in the 10 year post mTBI sample. A Network Comparison Test revealed evidence of a difference in network structure across the two samples (p = 0.045). However, the only symptoms that showed significant differences in strength centrality across samples were irritability and restlessness.ConclusionThe current findings suggest that frustration, blurred vision and concentration difficulties may have an influential role in the experience and maintenance of post-concussion symptoms. The impact of these symptoms may remain stable over time. Targeting and prioritising the management of these symptoms may be beneficial for mTBI rehabilitation

Assessing relative resilience potential of coral reefs to inform management

International audienceEcological resilience assessments are an important part of resilience-based management (RBM) and can help prioritize and target management actions. Use of such assessments has been limited due to a lack of clear guidance on the assessment process. This study builds on the latest scientific advances in RBM to provide that guidance from a resilience assessment undertaken in the Commonwealth of the Northern Mariana Islands (CNMI). We assessed spatial variation in ecological resilience potential at 78 forereef sites near the populated islands of the CNMI: Saipan, Tinian/Aguijan, and Rota. The assessments are based on measuring indicators of resilience processes and are combined with information on anthropogenic stress and larval connectivity. We find great spatial variation in relative resilience potential with many high resilience sites near Saipan (5 of 7) and low resilience sites near Rota (7 of 9). Criteria were developed to identify priority sites for six types of management actions (e.g., conservation, land-based sources of pollution reduction, and fishery management and enforcement) and 51 of the 78 sites met at least one of the sets of criteria. The connectivity simulations developed indicate that Tinian and Aguijan are each roughly 10 × the larvae source that Rota is and twice as frequent a destination. These results may explain the lower relative resilience potential of Rota reefs and indicates that actions in Saipan and Tinian/Aguijan will be important to maintaining supply of larvae. The process we describe for undertaking resilience assessments can be tailored for use in coral reef areas globally and applied to other ecosystems

XMM-Newton unveils the complex iron K alpha region of Mrk 279

We present the results of a ~160 ks-long XMM-Newton observation of the Seyfert 1 galaxy Mrk 279. The spectrum shows evidence of both broad and narrow emission features. The Fe K alpha line may be equally well explained by a single broad Gaussian (FWHM~10,000 km/s) or by two components: an unresolved core plus a very broad profile (FWHM~14,000 km/s). For the first time we quantified, via the "locally optimally emitting cloud" model, the contribution of the broad line region (BLR) to the absolute luminosity of the broad component of the Fe K alpha at 6.4 keV. We find that the contribution of the BLR is only ~3%. In the two-line component scenario, we also evaluated the contribution of the highly ionized gas component, which produces the FeXXVI line in the iron K region. This contribution to the narrow core of the Fe K alpha line is marginal <0.1%. Most of the luminosity of the unresolved, component of Fe K alpha may come from the obscuring torus, while the very-broad associated component may come from the accretion disk. However, models of reflection by cold gas are difficult to test because of the limited energy band. The FeXXVI line at 6.9 keV is consistent to be produced in a high column density (N_H~10^23 cm^{-2}), extremely ionized (log\xi~5.5-7) gas. This gas may be a highly ionized outer layer of the torus.Comment: 10 pages, 9 figures, accepted for publication in Astronomy and Astrophysic

LOFAR/H-ATLAS: The low-frequency radio luminosity - star-formation rate relation

Radio emission is a key indicator of star-formation activity in galaxies, but the radio luminosity-star formation relation has to date been studied almost exclusively at frequencies of 1.4 GHz or above. At lower radio frequencies the effects of thermal radio emission are greatly reduced, and so we would expect the radio emission observed to be completely dominated by synchrotron radiation from supernova-generated cosmic rays. As part of the LOFAR Surveys Key Science project, the Herschel-ATLAS NGP field has been surveyed with LOFAR at an effective frequency of 150 MHz. We select a sample from the MPA-JHU catalogue of SDSS galaxies in this area: the combination of Herschel, optical and mid-infrared data enable us to derive star-formation rates (SFRs) for our sources using spectral energy distribution fitting, allowing a detailed study of the low-frequency radio luminosity--star-formation relation in the nearby Universe. For those objects selected as star-forming galaxies (SFGs) using optical emission line diagnostics, we find a tight relationship between the 150 MHz radio luminosity ($L_{150}$) and SFR. Interestingly, we find that a single power-law relationship between $L_{150}$ and SFR is not a good description of all SFGs: a broken power law model provides a better fit. This may indicate an additional mechanism for the generation of radio-emitting cosmic rays. Also, at given SFR, the radio luminosity depends on the stellar mass of the galaxy. Objects which were not classified as SFGs have higher 150-MHz radio luminosity than would be expected given their SFR, implying an important role for low-level active galactic nucleus activity.Comment: 21 pages, 12 figures, accepted for publication in MNRA

Detection of blueshifted emission and absorption and a relativistic Iron line in the X-ray spectrum of ESO 323-G077

We report on the X-ray observation of the Seyfert 1 ESO323-G077 performed with XMM-Newton. The spectra show a complex spectrum with conspicuous absorption and emission features. The continuum emission can be modelled with a power law with an index of 1.99+/-0.02 in the whole XMM-Newton energy band, marginally consistent with typical values of Type-I objects. An absorption component with an uncommonly high equivalent Hydrogen column, n_H=5.82(+0.12/-0.11)x10^22 cm-2, is affecting the soft part of the spectrum. Additionally, two warm absorption components are also present. The lower ionised one has an ionisation parameter of Log(U)=2.14(+0.06/-0.07) and an outflowing velocity of v=3200(+600/-200) km/s. Two absorption lines located at ~6.7 and ~7.0 keV can be modelled with the highly ionised absorber. The ionisation parameter and outflowing velocity of the gas measured are Log(U)=3.26(+0.19/-0.15) and v=1700(+600/-400) km/s, respectively. Four emission lines were also detected in the soft energy band. The most likely explanation for these emission lines is that they are associated with an outflowing gas with a velocity of ~2000 km/s. The data suggest that the same gas which is causing the absorption could also being responsible of these emission features. Finally, the spectrum shows the presence of a relativistic iron emission line likely originated in the accretion disc of a Kerr BH with an inclination of ~25 deg. We propose a model to explain the observed X-ray properties which invokes the presence of a two-phase outflow with cone-like structure and a velocity of the order of 2,000-4,000 km/s. The inner layer of the cone would be less ionised, or even neutral, than the outer layer. The inclination angle would be lower than the opening angle of the outflowing cone.Comment: 11 pages, accepted in MNRA