In a study examining income and cholesterol levels, which method could researchers use to remove the influence of age on the correlation between these two variables?

The appropriate method for removing the influence of age on the correlation between income and cholesterol levels is partial correlation. Partial correlation allows researchers to understand the relationship between two variables while controlling for the effects of one or more additional variables—in this case, age.

By utilizing partial correlation, researchers can isolate the unique contribution of income to cholesterol levels, thereby providing a clearer picture of how these two variables are related without the confounding influence of age. This technique is particularly useful in observational studies where multiple factors can affect the relationship being examined.

Other correlation methods, such as Kendall's Tau and Spearman correlation coefficient, are useful for assessing the strength and direction of monotonic relationships, but they do not control for the influence of additional variables like age. The Point-Biserial correlation, which is used for measuring the relationship between a binary variable and a continuous variable, would not be applicable in this context as it does not address the need to control for another continuous variable. Thus, partial correlation is distinctly suited for the situation described in the question.