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On page 148 of the workbook there are two Matrices. Which plot the probabilities of x and y. Case 1 is the Indepedant case, case 2 is where the variables move in unison and therefore there is a positive correlation. Case 3 is where they move in opposition and are said to be negatively correlated. I can’t understand the difference between case 2 and 3 and why one is negative and the other positive. Could someone help please.
The way I think of it is as follows, this is just my intuitive way of looking at it, which may not be the best way.
A low value for X is 1 and a high value for X is 4. A low value for Y is 20, and a high value is 30. Consider the case where X=1 and Y=20, i.e., both are low values. If X and Y are independent (Case 1) we would expect 10% of observations to be in this cell, but in Case 2 it is more than that – it is 15%. Similarly when both X and Y are high (4, 30), the independent Case 1 indicates there should be 15% of observations in this cell, yet Case 2 shows it is more than that, i.e., 25%. In other words, for Case 2, when X is low then so is Y, and when X is high then so is Y. This is positive correlation.
Case 3 is the opposite. Take X=1 and Y=20. This shows 5%, which is less than the independent case where we would expect 10%. So when X is low, Y tends to be high. X and Y are negatively related.
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