Correlation R Squared
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R² is simply r squared, the correlation coefficient multiplied by itself. Since r ranges from -1 to 1, squaring it always produces a value between 0 and 1, and R² loses the information about the direction of the relationship.

R² represents the proportion of variance in one variable that's explained by the other, expressed as a fraction or percentage. An R² of 0.64 means 64% of the variability in the outcome can be statistically explained by the predictor.

A strong negative correlation, like r = -0.9, and a strong positive correlation, like r = 0.9, both square to the same R² of 0.81. This is intentional, since R² is meant to describe the strength of explanatory power, not the direction, which is why you should keep the original r if direction matters.

It depends heavily on the field: in controlled physical experiments, R² above 0.9 might be expected, while in social science or behavioral research, an R² of 0.3 can be considered meaningful given how many other factors influence human behavior. There's no single universal threshold for 'good.'

No, and this is one of the most common statistical misconceptions. R² only measures how well one variable statistically predicts or tracks another; a high R² can arise from a genuine causal link, a shared underlying cause, or pure coincidence.