Furthermore, [ 22] showed that the Z variables have the property to be the closest to X and Y, i.e. the sum of their squared multiple correlation coefficients with X and with Y is maximal.
Multiple correlation r Y, X1,..., X p ), measures the dependency of one model parameter Y on p other parameters X1,..., X p of the model.
In order to calculate the multiple correlation of Y and X1,..., X p within a sample of size n different runs for each parameter, all simple correlations r Y, X i must be determined using the Pearson correlation coefficient r Y, X i [ 81]: (13) r Y, X i = ∑ i = 1 n x i y i − n x ¯ y ¯ (∑ i = 1 n x i 2 − n x ¯ 2 ) (∑ i = 1 n y i 2 − n y ¯ 2 ).
using a sliding window approach (30 SNPs window size, 5 SNPs step size) and a VIF threshold of 1 x 10−6 (VIF = 1/(1−R ), where R is the multiple correlation coefficient for a SNP regressed on all other SNPs simultaneously).
To estimate correlation, multiple correlation coefficients were applied.
Now the multiple correlation coefficient can be easily found for any VM Xi by ( {R}_{X_{i,} {X}_{1,}dots dots {X}_{n-i},kern0.5em {X}_{n+i} dots dots.{X}_{n }kern0.5em }kern0.5em
The detail signals have weak multiple correlation, while the approximate signal has strong multiple correlation.
Linear multiple correlation, rank correlation, circular linear correlation, circular rank correlation, and multiple regression were used as statistical analyses.
4. Predicted multiple correlation coefficient value (0.9277) was in a reasonable good agreement with the adjusted multiple correlation value (0.9778). 5.
r, the multiple correlation coefficient, is the linear correlation between the observed and model-predicted values of the dependent variable.
