Regression R2 vs Spearman's correlation

#1
Hi everyone!
I have a set of data that shows a very good Spearman's correlation coefficient (p=0,001), but when i calculate a regression equation (linear or not), my R2 is rather low (around 0.5). How do I obtain an equation with a good fit that explains this correlation and allows me to predict data?
thank you!
 

gianmarco

TS Contributor
#2
Hi !
Firstly, I have not a deep math knowledge, so take my words with one or two grains of salt :D

Secondly:
1) you should provide use with some more info about your data;
2) I am wondering why you used spearman and then switched to another kind of measure of association
3) do you data meet the assumptions of linear correlation?
4) what value of Spearman's r did you get from your data?

Whit these questions in mind, may be that your two varialbles are monotonically related (this would explain the significant rs; but I would like to know what is the value of rs) but the relationship is not linear (this would explain the R2 value). See this page for further info about Spearman vs Pearson correlation:
http://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient

Hoping that this can help you a bit
Regards,
Gm
 

Dragan

Super Moderator
#3
Hi everyone!
I have a set of data that shows a very good Spearman's correlation coefficient (p=0,001), but when i calculate a regression equation (linear or not), my R2 is rather low (around 0.5). How do I obtain an equation with a good fit that explains this correlation and allows me to predict data?
thank you!
Are you aware of the fact that when you regress the rank of Y (RY) on the rank of X (RX) -- or vice versa -- that the regression weight (or slope coefficient) is the Spearman correlation coefficient.
 
#4
For your Spearman test you give a significance (P-value) but for your Pearson test you give a strength (r-value). It is perfectly possible for an association to be very weak (e.g. r^2 much less than 0.5) and still very significant (e.g. P-value even lower than 0.001). Stregth is not the same as significance! If you really want to compare the results of a Pearson and Spearman test, please give us comparable numbers for each: either r and rho, or P values for both.

It is certainly possible for a Spearman association to be strong when a Pearson association is weak. That just means that the association is highly non-linear.

Given the results of a Spearman test, it is not possible to write a regression equation which predicts Y as a function of X. You could write an equation which predicts the rank of Y as a function of the rank of X, but that is presumably not what you are looking to do.