I ran a regression and I have trouble understanding the interpretation of a coefficient if I have some independent variables that are proportions. I ran a FE regression btw, so I know that the interpreation would be something like "for a given fund, as X varies
across time by one unit, Y changes by 𝛽2 units".
The dependent variable in my regresson is i.e. excess returns like i.e. "2.5" (or -1.7 etc.). As independent variable I know i.e. have "Members-to-beneficiaries-ratio" expressed as i.e. "0.77" or "3.5" or even "125.8" etc. So, for a given fund, as the Members-to-beneficiaries-ratio varies across time by one unit, the excess return changes by i.e. - .345 units. Does this mean if in my first example the MtBRatio changes from 0.77 to 1.77 then the excess return changes from 2.5 to 2.155?
Any help on this would be greatly appreciated! Thanks a lot in advance.
I'll take a shot at this question. Fist the meaning of a regression.coefficient never changes .it is the change in y divided by the change in x. As x-->0 whatever the units might be. Thus the units will be unit of y on.top and units of x on the bottom.
This is all one .needs to know about the topic. Please note that 8%--6%=2%. Further 8%/ 4%= 2 One can convert to more convenient units as needed. YOU MUST KEEP TRACK OF THE UNITS. BTW old chemists call this dimensional analysis. Best wishes, David Booth
Oops the above should say as change in x ---
-->0
Mea culpa, David Booth
As professor Booth said, there is no change in the way of interpretation.
Thanks for your input David Eugene Booth & Babak Jamshidi . I just tried to make sense out of what you were saying but I think I still struggle to understand exactly what you mean. I have been reading about units and dimensional analysis too. Sorry I have to ask for further elaboration.
So if I have i.e. 2.5 (y) / 0.77 (x) then my unit rate is = 2.5 / 0.77. This 0.77 is basically a ratio. But the way I get it then is: 2.5 + (-0.345)/ 0.77 + (2.5/0.77). But this seems for me rather difficult to put in words when interpreting the results.
Not sure if I am just not making the link here and am confused because I use a ratio instead of just a regular number (as i.e. just number of members/beneficiaries).
Averagely, one percent increase in the proportion of (IV) leads to 0.3 meters drop in the height of the... I think it is a good example to illustrate what you need.
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