A useful way to understand how correlation works is to modify a set of contrived data. Run a correlation analysis on the following set of ten bivariate data, given as the values of (X,Y) for each unit: (1,5) (2,6) (3,4) (4,5) (5,5) (6,4) (7,6) (8,5) (9,6) (10,4).
(a) What is the value of the correlation coefficient? (You might draw a scatter plot of the data to help visualise the relationship.)
(b) Next, modify some of the Y values only to give a highly significant positive correlation between X and Y. Here a scatter plot might help you decide how to do this.
(c) Finally, modify some of the Y values only to give a highly significant negative correlation between X and Y.