Explore BrainMass

Partial Correlation

Partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed. The partial correlation between X and Y given a set of n controlling variables Z = {Z1, Z2,…,Zn}, is the correlation between the residuals RX and RY resulting from the linear regression of X with Z and of Y with Z. The first order partial correlation is nothing else than a difference between a correlation and the product of the removable correlations divided by the product of the coefficient of alienation of the removable correlations. A simple way to compute the partial correlation for some data is to solve the two associated linear regression problems, get the residuals and calculate the correlation between the residuals.

The semi-partial correlation statistic is similar to the partial correlation statistic. Both measure variance after certain factors are controlled for, but to calculate the semi-partial correlation one holds the third variable constant for either X or Y. Whereas for partial correlations one holds the third variable constant for both. This correlation is viewed as ore practically relevant. It is less theoretically useful however, because it is less precise about the unique contribution of the independent variables. 

Confusing Correlation and Causation

Find an article in a newspaper, magazine or on the internet that confuses correlation and causation. Give a brief summary of the article and explain why you chose this article. For the article above, list other variables that could contribute to the relationship between the two variables.

Correlation Coefficient with Scatterplot

An investigator at a diet center is interested in the habits of clients entering his center's weight loss program. Given the pairs of observations below, where X = number of hours per week spent watching television and Y = number of pounds gained in the past year: a) Construct the scatterplot, (but first read d and e below).