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The GQS appears to be a reliable method because of the relatively low coefficients of variation (ranging from 14.1 to 22.4%) for CH4 emissions and a moderate relationship (coefficient of determination = 0.42) between CH4 emissions and DMI.
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In the SVN and SVW respiratory tests (except for the SVN test of the first dog), results showed a moderate relationship, but, in general, correlation coefficients estimated in TM signal were better than estimations in FL and DP signal.
Since a correlation coefficient of greater than 0.60 implies a moderate relationship between variables [ 20], 0.60 was used as an indicator of the potential for multicollinearity.
The correlation coefficient between the two dimensions of 0.56 suggests a moderate relationship.
Interpretation of correlation coefficients was as follows: r ≤ 0.49, weak relationship; 0.50 ≤ r ≤ 0.74, moderate relationship; and r ≥ 0.75, strong relationship [ 29].
To describe the strength of the correlation, we used the Salkin scale for the absolute value of the correlation coefficient (r): very strong relationship (0.80 ≤ r ≤ 1.0), strong relationship (0.60 ≤ r < 0.80), moderate relationship (0.4 ≤ r < 0.6), weak relationship (0.2 ≤ r < 0.4), and very weak or no relationship (0.20 < r ≤ 0).
Correlation coefficients of 0.1 to 0.3 were considered to indicate a weak relationship, 0.3 to 0.5 a moderate relationship and > 0.5 a strong relationship.
Absolute value of correlation coefficient (r) from 0 to 0.25, ≥0.25 and <0.5, ≥0.5 and <0.75, and ≥0.75 was considered little or no relationship, a fair degree of relationship, a good or moderate relationship, and a very good to excellent relationship, respectively.
To interpret the magnitude of the correlation coefficients ρ, the following guidelines from [28] were followed: for absolute values between 0 and 0.19 a very slight relationship, between 0.20 and 0.39 a slight one, between 0.40 and 0.59 moderate relationship, between 0.60 and 0.79 a strong one, and between 0.80 and 1 very strong.
Methods to separate pedigree relationships sharing the same relationship coefficient have been proposed.
Regression analysis between temperature and vegetation shows a moderate regression coefficient value of 0.5751 (Fig. 6a) and exhibited a significant relationship.
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