On the use of <i>r</i> and <i>r</i> squared in correlation and regression

Kasuya, Eiiti

doi:10.1111/1440-1703.1011

Cited by 94 publications

(46 citation statements)

References 4 publications

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“…Also, the relationship between each independent and dependent variable is analyzed using the regression coefficient. Besides, the coefficient of determination was also assessed, which is also denoted by R-squared value; R 2 is the fraction of variation of one variable explained by other variables used to determine the strength of the relationship in the regression model (Kasuya 2018). Therefore, the higher R-squared value in this study indicates that the model fits the data well.…”

Section: Discussionmentioning

confidence: 98%

Reduction in concentration of PM2.5 in India’s top most polluted cities: with special reference to post-lockdown period

Roy

Singha

2021

Air Qual Atmos Health

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Section: Discussionmentioning

confidence: 98%

Reduction in concentration of PM2.5 in India’s top most polluted cities: with special reference to post-lockdown period

Roy

Singha

2021

Air Qual Atmos Health

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“…All correlation analyses were done based on the Pearson correlation coefficient of which the statistical significance was evaluated with a two-sided t-test at a confidence level of 95%. The squared Pearson correlation coefficient (R 2 ) is equal to the coefficient of determination in the special case of linear regression with one explanatory variable and an intercept term (Devore, 2011;Kasuya, 2019).…”

Section: Data Processing and Statistical Analysismentioning

confidence: 99%

Canopy structure explains the relationship between photosynthesis and sun-induced chlorophyll fluorescence in crops

Dechant

Ryu

Badgley

et al. 2020

Remote Sensing of Environment

227

171

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Remote sensing of far-red sun-induced chlorophyll fluorescence (SIF) has emerged as an important tool for studying gross primary productivity (GPP) at the global scale. However, the relationship between SIF and GPP at the canopy scale lacks a clear mechanistic explanation. This is largely due to the poorly characterized role of the relative contributions from canopy structure and leaf physiology to the variability of the top-of-canopy, observed SIF signal. In particular, the effect of the canopy structure beyond light absorption is that only a fraction (f esc) of the SIF emitted from all leaves in the canopy can escape from the canopy due to the strong scattering of near-infrared radiation. We combined rice, wheat and corn canopy-level in-situ datasets to study how the physiological and structural components of SIF individually relate to measures of photosynthesis. At seasonal time scales, we found a considerably strong positive correlation (R 2 =0.4-0.6) of f esc to the seasonal dynamics of the photosynthetic light use efficiency (LUE P), while the estimated physiological SIF yield was almost entirely uncorrelated to LUE P both at seasonal and diurnal time scales, with the partial exception of wheat. Consistent with these findings, the canopy structure and radiation component of SIF, defined as the product of APAR and f esc , explained the relationship of observed SIF to GPP and even outperformed GPP estimation based on observed SIF at two of the three sites investigated. These results held for both half-hourly and daily mean values. In contrast, the total emitted SIF, obtained by normalizing observed SIF for f esc , improved only the relationship to APAR but considerably decreased the correlation to GPP for all three crops. Our findings demonstrate the dominant role of canopy structure in the SIF-GPP relationship and establish a strong, mechanistic link between the near-infrared reflectance of vegetation (NIR V) and the relevant canopy structure information contained in the SIF signal. These insights are expected to be useful in improving remote sensing based GPP estimates.

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“…As seguintes métricas de avaliação foram utilizadas: o Erro Absoluto Médio (EAM), a Raiz do Erro Quadrático Médio (REQM) e o R-quadrado (R 2 ). O EAM correspondeà média absoluta da distância entre os valores previstos e os valores reais, o que permite uma melhor interpretação do erro na prática; o REQM corresponde ao desvio padrão médio da amostra utilizada, permitindo entender o quão capaz o regressoré para realizar boas predições [Silva et al 2017] e o R 2 corresponde a proporção de variação de uma variável (variável objetiva) explicada por outras variáveis (variáveis explicativas) em regressão, o que permite a interpretação do quão bom o modeloé ao prever dados a partir das variáveis preditoras [Kasuya 2019].…”

Section: Resultsunclassified

Planejamento Cirúrgico de Estrabismo Horizontal Utilizando Árvore de Regressão de Múltiplas Saídas

Leite¹,

Almeida²,

Teixeira³

et al. 2020

Anais Principais Do Simpósio Brasileiro De Computação Aplicada À Saúde (SBCAS 2020)

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O estrabismo e uma patologia oftalmológica que afeta entre 1,55% e 3,6% da população, que pode causar danos sensoriais irreversíveis à visão. O tratamento dos casos mais graves requer intervenção cirúrgica. Desta forma, este trabalho utiliza Árvores de Regressão aplicadas em forma de única saída e múltiplas saídas para indicar o planejamento de cirurgias de estrabismo. Em nosso método mais preciso, Multi-Target Regression Trees, em uma abordagem em única saída, foi obtido o Erro Absoluto Médio de 0,49 milímetros, a Raiz do Erro Quadrático Médio de 1,49 milímetros e R2 de 0,65 na indicação do plano cirúrgico de estrabismos horizontais.

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On the use of r and r squared in correlation and regression

Abstract: Notations for coefficients in correlation and regression are discussed. r or R, not r squared or R squared, is inappropriate to denote the coefficient of determination because of the risk of the confusion with other coefficients with different meanings.

Cited by 94 publications

References 4 publications

Reduction in concentration of PM2.5 in India’s top most polluted cities: with special reference to post-lockdown period

Reduction in concentration of PM2.5 in India’s top most polluted cities: with special reference to post-lockdown period

Canopy structure explains the relationship between photosynthesis and sun-induced chlorophyll fluorescence in crops

Planejamento Cirúrgico de Estrabismo Horizontal Utilizando Árvore de Regressão de Múltiplas Saídas

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