About R and R² Correlations
Two main statistics used in this website are r, which is Pearson's correlation coefficient, and R² which is the coefficient of determination.
Pearson's r measures the linear relationship between two variables and is always between -1 and +1; -1 means a perfect negative relationship and +1 mean a perfect positive relationship. An example of a positive relationship in crop agriculture is that as vegetation increases the amount of near infrared reflectance increases. An example of a negative relationship in crop agriculture is that as vegetation increases the amount of visible wavelength reflectance decreases (until saturation). An important characteristics of Pearson's r is that it conveys whether a relationship is positive or negative.
The coefficient of determination, R², equals Pearson's r squared in a linear relationship. In regards to data in this website the R² will always be between 0 and +1 (an adjusted coefficient of determination can be negative but that does not apply to data in this website). In regards to the information in this website, R² can be viewed as the proportion (percent) of variability in the data that is accounted for by the predictive model, divided by 100. For example, regarding the ability of Landsat to predict yield spatial patterns, if an R² value is listed as 0.7142, then 71.42% of the yield spatial patterns are predicted by Landsat.
The level of significance is an important characteristic of a correlation. The P-value is related to the level of significance. Student's p-values for correlations are shown in this website and are typically < 0.0001. The lower the p-value, the more significant the relationship; if the p-value is very low, such as < 0.0001, the correlation is highly significant. (Student’s p-values are calculated here based on n-2 degrees of freedom from the t-distribution.)