Regression: Standard Error of the mean interpretation?

el1

New Member
#1
Im not sure how to interpret the Syx.

I have a Syx of 4.1037.

So far i can tell to say ,

the Syx is relatively small in relation to ....

Then im stuck lol.

The distribution on the scatter graph around the regression line seem to be quite close to the line but scattered about.

Can anyone help?
 

Dragan

Super Moderator
#2
Im not sure how to interpret the Syx.

I have a Syx of 4.1037.

So far i can tell to say ,

the Syx is relatively small in relation to ....

Then im stuck lol.

The distribution on the scatter graph around the regression line seem to be quite close to the line but scattered about.

Can anyone help?

Perhaps you might want to consider the Syx in relation to the standard deviation of Y (Sy).

Look, the standard error for a regression line (Syx) associated with the regression of Y on X can be determined as:


Syx = Sy*Sqrt[ (1 - R^2)*((N -1)/(N-2)) ].


Thus, you can see that Syx is a funtion of Sy. So, if Syx is small relative to Sy than you can say that you're getting help in predicting Y using X because Y and X are correlated. On the other hand, if there is no correlation between Y and X then Syx is going to be approximately equal to Sy. Further,
as N -> Infinity then Syx = Sy (if Ryx=0).