Final answer:
Correlations, as cosines of angles in factor analysis, help to measure the strength and direction of the relationship between variables using a correlation coefficient. A positive or negative correlation indicates how two variables change together, but this does not confirm causation.
Step-by-step explanation:
The fact that correlations correspond to the cosines between angles has been instrumental for researchers using factor analysis. This relationship allows researchers to evaluate the degree of association between variables. A correlation coefficient, developed by Karl Pearson, is a measurement from -1 to +1 that signifies the strength and direction of the relationship between two variables. A positive correlation suggests that as one variable increases, so does the other; a negative correlation indicates that as one variable increases, the other decreases.
It is important, however, to note that Correlation Does Not Indicate Causation. In other words, just because two variables are correlated does not mean that one causes the other. There could be confounding variables affecting the correlation. This understanding is critical in fields such as physics, where researchers often analyze the correlation between various physical quantities, and geography, where geographers may analyze correlations between variables like fast food density and obesity rates to identify trends and relationships.