Pearson’s correlation

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... 

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. 

SED-TOX scores were determined for each sediment sample investigated in the two studies and Pearson s correlations were estimated with benthic community metrics and levels of contamination (SAS, 1988). Contamination levels were expressed as the mean ratios of individual contaminant concentrations in a sample relative to their respective SQG values. Logarithmic transformations were applied to mean SQG quotient values to respect the assumption of normality. 

Bivariate statistics. The objective here is to look for possible relationships between pairs of variables. Pearson s correlation has traditionally been the most used, although the analysis of the correlation matrix should be studied before the use of most multivariate statistical procedures. 

The mean concentration of IGF-I in follicular fluid was 129 67 ng/ml (mean SD). Linear regression analysis showed that IGF-I concentrations were significantly and inversely correlated with both the number of ampoules of FSH administered (Pearson s correlation coefficient = —0.405, p = 0.001) and with the number of days of FSH administration (Pearson s correaltion coefficient = -0.249, p = 0.039). 

From Pearson s correlation coefficients, we noted a negative weak correlation between methemoglobin and antioxidant enzymes for the N group (r = -0.35 for... 

Accepting normal bivariate distribution, Pearson s correlation coefficient, defined... 

Table 13.10 Pearson s correlation coefficients between the color parameters and phenolic components...

The effect of variability on the overall performance of the method was assessed by adding an error term to X and Y in each run of the simulation as described earlier (see step 3). After a large number of data points were simulated for each set of alternative method and in vivo test CVs, the Pearson s correlation coefficient was calculated in order to determine the correlation between the X and Y values. A second set of X values ranging from 0 to 40 were also run to simulate results for eye irritation scores that might be observed with a more restricted set of test substances such as cosmetics products. 

Table 4 Expected Pearson s correlation coefficients when the error in vivo and alternative method data are considered...

Pearson s correlation coefficient can in general be used for the purpose (Duggan et al, 1999). If a cut-off criteria of 0.9 (-0.9 represents negative correlation while 0.9 represents positive correlation) is taken for highly... 

Pearson s correlation coefficient statistical indices (O correlation measures)... 

Several different correlation measures were proposed, depending on the nature of data. Pearson s correlation coeflBdent. It is the most known bivariate correlation measure estimating the degree of association between the two variables j and k, as follows ... 

Sheiner and Beal (1981) have pointed out the errors involved in using the correlation coefficient to assess the goodness of fit (GOF) in pharmacokinetic models. Pearson s correlation coefficient overestimates the predictability of the model because it represents the best linear line between two variables. A more appropriate estimator would be a measure of the deviation from the line of unity because if a model perfectly predicts the observed data then all the predicted values should be equal to all the observed values and a scatter plot of observed vs. predicted values should form a straight line whose origin is at the point (0,0) and whose slope is equal to a 45° line. Any deviation from this line represents both random and systemic error. 

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