Pearson’s coefficient

In order to eliminate parameters that are correlated to each other, we calculate their Pearson correlation coefficients (25). Linearly uncorrelated parameters have Pearson correlation coefficients close to zero and likely describe different aspects of the phenotype under study (exception for non-linearly correlated parameters which cannot be scored using Pearson s coefficient). We have developed an R template in KNIME to calculate Pearson correlation coefficients between parameters. Redundant parameters that yield Pearson correlation coefficients above 0.4 are eliminated. It is important to visually inspect the structure of the data using scatter matrices. A Scatter Plot and a Scatter Matrix node from KNIME exist that allow color-coding the controls for ease of viewing. 

In the review of results for 2008 (results not published), the values for ALA-D in the adult sample were 60.59 16.49 (x + SD), higher than those obtained in 1990 46.81 15.45 (x SD), which is logical if we take into account the fact that the activity of ALA-D in erythrocytes has a negative or inverse correlation with respect to the concentration of Pb in blood. In the 1990 study, Pearson s coefficient of linear correlation obtained was r = -0.568... 

Another useful measure of the regression model is Pearson s coefficient of regression, R. It can be calculated as follows ... 

Calculating Pearson s Coefficient of Regression The closer the value is to one, the better the regression is. This coefficient gives what fraction of the observed behaviour can be explained by the given variables. 

Figure 5.15 shows the measured and predicted mean summer temperatures as a function of time. It can be seen that the model does follow the trends in the data well. However, it does not predict well the extreme values. Booking at this plot it seems quite clear that there is a seasonal component to the occurrence of extreme values. The fit as determined by Pearson s coefficient of regression is 32.04%. 

Speed [pixels/frame] s.d. Mean of the direction [°] confidence interval Pearson s coefficient r of directionality... 

Conversely, it is also possible to analyze the directionality of a population moving at a high speed. In Fig. 10a, only the vectors with a speed between 1 and 2 pixels per frame are shown (see also Fig. 10b). The movement direction of this high speed population was clearly outward, as it is evident in the histogram shown in Fig. 10c,d. Table 2 is the summary of these filtering and analyses. Mean value of the movement direction was calculated by von Mises circular statistics [58]. Pearson s coefficient r is a concentration parameter for the directionality, r is 0 when the direction is randomly oriented and 1 when the movement is confined in a single direction. Increase in the precision of the measurement is reflected in an increase in the Pearson s coefficient r. 

The Pearson s coefficient, R, describes the correlation between the intensity levels and distribution between two channels in terms of a least-squares fit. R can fell between -1 and 1, where -1 indicates complete exclusion and 1 indicates complete correlation between two channels. Values between 0 and 1 indicate a proportional degree of overlap between two channels, and values between -1 and 0 are ambiguous, indicating some form of inverse relationship between the channels. Manders coefficient fells between 0 and 1, which indicate complete exclusion and complete correlation, respectively, between two channels. 

Correlations of Pearson s coefficient (r or r ) values of between 0.77 and 0.98 have been reported between BOD and peaks T and (Reynolds and Ahmad, 1997 Ahmad and Reynolds, 1999 Baker, 2001 Ahmad et al., 2002 Hudson et al., 2008 Hur et al., 2008). The correlations of peaks Aq and C (which represent humic and fulvic-like fluorescence) with the 5-day BOD were lower (r = 0.72-0.77) (Baker, 2001 Hudson et al., 2008). The strong correlation between the 5-day BOD and the tryptophan-like fluorescence at around 340-350 nm is expected, as BOD is an indirect measure of miCTobial growth. Furthermore, the tryptophan-like fluorescence has been associated with wastewater microbial activity (Reynolds, 2002 Elliott et al., 2006 Hudson et al., 2008), whereas fulvic and humic-like fluorescence has been reported to represent the nonreadily biodegradable organic fraction of wastewaters (Reynolds, 2002). 

It is also important to check for correlations between the descriptors. Highly correlated descriptors could lead to the information that they encode being over-represented. A straightforward way to determine the degree of correlation between two properties is to calculate a correlation coefficient. Pearson s correlation coefficient is given by ... 

Correlation coefficient. In order to establish whether there is a linear relationship between two variables xx and the Pearson s correlation coefficient r is used. 

Pearson s correlation coefficient of different robust PCA scores is usually not zero. 

Matrix B consists of q loading vectors (of appropriate lengths), each defining a direction in the x-space for a linear latent variable which has maximum Pearson s correlation coefficient between y and jf for j = 1,..., q. Note that the regression coefficients for all y-variables can be computed at once by Equation 4.52, however,... 

FIGURE 2 Retention factors on two chromatographic systems (a) dissimilar CS, (b) similar CS, and (c) similar CS with some atypical correlation results, r = Pearson s correlation coefficient. 

A question of interest is the possible existence of correlations between and Sgc skews in intronic sequences without repeats. When all genes are considered, only small correlation is observed (Pearson s correlation coefficient r equals 0.09). However, the values of the skews from small genes turn out to be highly noisy. When one excludes these small genes, 5ta and Sgc present larger correlation (e.g., r = 0.45) for genes with total intron length I > lOkbp and... 

Fields can be utilized in virtual screening applications for assessing the similarity (alignment) or complementarity (docking) of molecules. Two similarity measures have achieved the most attention. These are the so-called Garbo- [195] and Hodgkin indexes [196] respectively. Others are Pearson s product moment correlation coefficient [169] and Spearman s rank correlation coefficient [169]. 

It is important to know the effectiveness of the model for predicting values however, it is also important to know the strength of the linear relationship between the two variables (known and predicted) being studied. This is achieved using the linear correlation coefficient (Pearson s product moment correlation coefficient), r, as a descriptive measure for the strength of the linear relationship (straight line) between the two variables ... 

The Pearson s correlation coefficient (r) gives an insight into how well a linear model fits the dataset in other words, how much of the activity can be explained by a linear model ". The closer r2 is to 1, the better the model is. An r2 of 0.89, for instance, means that 89% of the variance is explained by the linear model. 

The Spearman correlation coefficient works in essentially the same way as Pearson s. Its value can be anything between —1 and +1. Zero represents no correlation and the extreme values either perfect negative or perfect positive correlation. In this case, a Spearman correlation coefficient of +0.748 indicates quite a strong relationship. The P value is strongly significant, so it looks as if we were wasting our money when we hired the consultant (how unusual is that ). 

Another measure of interest is the sample correlation coefficient, or Pearson s r, or Pearson s133 product-moment formula, or the linear correlation of xand y ... 

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