Teilkorrelation

Teilkorrelation, also known as partial correlation, is a statistical measure that quantifies the linear relationship between two variables while controlling for the influence of one or more other variables. In essence, it isolates the unique association between a pair of variables by removing the shared variance that might be explained by a third variable.

The concept of partial correlation is particularly useful in situations where multiple factors might be influencing the observed relationship between two primary variables. For example, if we are examining the relationship between hours studied and exam scores, we might also consider intelligence as a potential confounding variable. A high level of intelligence could independently lead to both more study time and better exam performance, creating a spurious correlation between study time and scores. Partial correlation allows us to assess the relationship between study time and exam scores *after* accounting for the effect of intelligence.

The calculation of partial correlation involves a series of regression analyses. First, each of the two variables of interest is regressed onto the control variable(s). The residuals from these regressions represent the variance in each variable that is *not* explained by the control variable(s). The partial correlation is then the simple Pearson correlation coefficient calculated between these residuals. A positive partial correlation indicates that as one variable increases, the other tends to increase, even after controlling for the shared influence of other factors. A negative partial correlation suggests an inverse relationship. A partial correlation close to zero implies that any observed linear relationship between the two variables is largely or entirely due to the influence of the control variable(s). This technique is a valuable tool in exploratory data analysis and in building more robust causal models.