An Investigation of the Median-Median Method of Linear Regression

Walters, Elizabeth; Morrell, Christopher H.; Auer, Richard E.

doi:10.1080/10691898.2006.11910582

Cited by 9 publications

(5 citation statements)

References 7 publications

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“…Here it seems that the student imagined drawing the line through points which are midpoints of different clusters of points. This is quite similar to the reasoning used for the medianmedian line (Walters et al 2006, Wilson 2010. The concept of average of all the points can be used as a springboard to a discussion of the least squares line.…”

Section: ᭜ Student Responses To the Tasks ᭜mentioning

confidence: 63%

Understanding Student Attempts to Find a Line of Fit

Sorto

White

Lesser

2011

Teaching Statistics

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Section: ᭜ Student Responses To the Tasks ᭜mentioning

confidence: 63%

Understanding Student Attempts to Find a Line of Fit

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White

Lesser

2011

Teaching Statistics

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“…Next, to evaluate changes in species’ phenology over the study period, we assessed each taxon separately with median-based linear models, as this method is robust to outliers 77 . Time was the explanatory variable, and phenological descriptors were the responses.…”

Section: Methodsmentioning

confidence: 99%

Species traits affect phenological responses to climate change in a butterfly community

Zografou

Swartz

Adamidis

et al. 2021

Sci Rep

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Diverse taxa have undergone phenological shifts in response to anthropogenic climate change. While such shifts generally follow predicted patterns, they are not uniform, and interspecific variation may have important ecological consequences. We evaluated relationships among species’ phenological shifts (mean flight date, duration of flight period), ecological traits (larval trophic specialization, larval diet composition, voltinism), and population trends in a butterfly community in Pennsylvania, USA, where the summer growing season has become warmer, wetter, and longer. Data were collected over 7–19 years from 18 species or species groups, including the extremely rare eastern regal fritillary Speyeria idalia idalia. Both the direction and magnitude of phenological change over time was linked to species traits. Polyphagous species advanced and prolonged the duration of their flight period while oligophagous species delayed and shortened theirs. Herb feeders advanced their flight periods while woody feeders delayed theirs. Multivoltine species consistently prolonged flight periods in response to warmer temperatures, while univoltine species were less consistent. Butterflies that shifted to longer flight durations, and those that had polyphagous diets and multivoltine reproductive strategies tended to decline in population. Our results suggest species’ traits shape butterfly phenological responses to climate change, and are linked to important community impacts.

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“… Wald’s (1940) ideas likely generated sufficient interest in using the median rather than the mean for fitting linear regressions. Subsequently, other researchers have expanded on using the median to circumvent the problems caused by outliers when fitting regressions ( Walters et al, 2006 ). However, more elaborated methods based on different measurements of scale and location ( Andrews et al, 1972 ) with higher breakdown values were developed to ignore or minimize the impact of outliers on the parameter estimates of regressions, including quantiles, winsorized mean, trimmed mean, M-measures with diverse influence functions (e.g., Huber, Andrews, Hampel, and biweight) to list a few.…”

Section: Competitive Advantage In Animal Production Systemsmentioning

confidence: 99%

ASAS-NANP Symposium: Mathematical Modeling in Animal Nutrition: The progression of data analytics and artificial intelligence in support of sustainable development in animal science

Tedeschi

2022

Journal of Animal Science

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A renewed interest in data analytics and decision support systems in developing automated computer systems is facilitating the emergence of hybrid intelligent systems by combining artificial intelligence (AI) algorithms with classical modeling paradigms such as mechanistic modeling (HIMM) and agent-based models (iABM). Data analytics have evolved remarkably, and the scientific community may not yet fully grasp the power and limitations of some tools. Existing statistical assumptions might need to be re-assessed to provide a more thorough competitive advantage in animal production systems towards sustainability. This paper discussed the evolution of data analytics from a competitive advantage perspective within academia and illustrated the combination of different advanced technological systems in developing HIMM. The progress of analytical tools was divided into three stages: collect and respond, predict and prescribe, and smart learning and policy-making, depending on the level of their sophistication (simple to complicated analysis). The collect and respond stage is responsible for ensuring the data is correct and free of influential data points, and it represents the data and information phases for which data is cataloged and organized. The predict and prescribe stage results in gained knowledge from the data and comprises most predictive modeling paradigms, and optimization and risk assessment tools are used to prescribe future decision-making opportunities. The third stage aims to apply the information obtained in the previous stages to foment knowledge and use it for rational decisions. This stage represents the pinnacle of acquired knowledge that leads to wisdom, and AI technology is intrinsic. Although still incipient, HIMM and iABM form the forthcoming stage of competitive advantage. HIMM may not increase our ability to understand the underlying mechanisms controlling the outcomes of a system, but it may increase the predictive ability of existing models by helping the analyst explain more of the data variation. The scientific community still has some issues to be resolved, including the lack of transparency and reporting of AI that might limit code reproducibility. It might be prudent for the scientific community to avoid the shiny object syndrome (i.e., AI) and look beyond the current knowledge to understand the mechanisms that might improve productivity and efficiency to lead agriculture towards sustainable and responsible achievements.

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An Investigation of the Median-Median Method of Linear Regression

Cited by 9 publications

References 7 publications

Understanding Student Attempts to Find a Line of Fit

Understanding Student Attempts to Find a Line of Fit

Species traits affect phenological responses to climate change in a butterfly community

ASAS-NANP Symposium: Mathematical Modeling in Animal Nutrition: The progression of data analytics and artificial intelligence in support of sustainable development in animal science

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