Pearson’s coefficient of regression

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%. 

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,... 

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). 

Our data were submitted to descriptive analysis in terms of mean values, range and frequency distributions. Since the distributions of lead exposure parameters were skewed, a log transformation of values was applied. Pearson s correlation coefficients were calculated to evaluate the association between neuropsychological impairments and lead exposure. The level of significance assumed was p < 0.05 (one-tailed). To evaluate the influence of potential confounding variables on measured parameters, analysis of variance (ANOVA) was performed. In addition, we estimated the variance of psychometric tests explained by covariates (ALA-D, PbB, PbH, PbT) after regressing out the effects of demographic variables (ANCOVA). 

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