2

EDIT: I was reading : Why is correlation not very useful when one of the variables is categorical?

When I thought of the issue of correlation between two continuous variables X,Y , when one of them is not stochastic ( obviously at least one of the two must be stochastic), as in ,e .g., hours studied/week vs GPA or hours of exercise vs blood pressure. Here standard correlation does not seem to say much: If X is not stochastic, it does not in any way depend on Y. Is any other concept used in this case?

MSIS
  • 447
  • 3
  • 10

1 Answers1

2

Here standard correlation does not seem to say much: If X is not stochastic, it does not in any way depend on Y.

Y can still depend on X, though. In that case correlation can still make sense but typically people will look to regression-like methods for describing the relationship (which encompasses correlation). However, be aware of omitted variable bias

since X does not depend on Y, we end up with Corr(X,Y) $\neq$ Corr(Y,X)?

Correlation is a symmetric measure - if you interchange x and y the correlation is unchanged.

 x=1:10               # fixed x
 y=3+0.1*x+rnorm(10)  # y depends on x
 cor(x,y)
[1] 0.6765819
 cor(y,x)
[1] 0.6765819
Glen_b
  • 257,508
  • 32
  • 553
  • 939
  • But then hours of study are related to GPA? Or change in GPA affects hours of study? – MSIS Nov 09 '19 at 00:42
  • I mean, I understand the Mathematics behind it but these don't seem to reflect the fact that a change in GPA does not lead to a change in hours of study. – MSIS Nov 09 '19 at 00:56
  • 1
    You seem to be confusing association with causation. Correlation is not causation. If GPA is related to amount of study, amount of study is related to GPA. – Glen_b Nov 09 '19 at 01:00
  • No, clearly there is no causation, but I am having trouble even seeing an association between the two. – MSIS Nov 09 '19 at 01:02
  • 1
    If more study implies higher GPA, then the higher GPAs will have a higher proportion of students who study more – Glen_b Nov 09 '19 at 01:05
  • Fair enough. Thanks, Glen_b – MSIS Nov 09 '19 at 01:06
  • 1
    @MSIS - Instead of reasoning on causation I would suggest reasoning on prediction. If correlation is high, we can predict that somebody with higher GPA has studied more hours and we will tend to be right. – Pere Nov 09 '19 at 14:48
  • Ok, I see it as a sort of contrapositive. – MSIS Nov 12 '19 at 01:14