Simple correlation
Measures the raw relationship between X and Y without controlling anything else.
Controlled correlation
Partial Correlation
Partial correlation asks whether X and Y are still related after removing the influence of a third variable. It is useful when a simple correlation may be driven by a confounder.
Control variable
Removes the shared influence of a third variable, such as age, income, or baseline skill.
Partial correlation
Shows the remaining relationship between X and Y after the control variable is accounted for.
Why this matters
If a correlation disappears after controlling a third variable, the original relationship may not be direct. If it remains strong, the relationship is harder to dismiss as a simple confounding artifact.
Context
Correlation vs causation
Control variables help, but they still do not prove causation by themselves.
Interpretation
R² and explained variance
Use R² to understand how much variation a relationship explains.