Model Ratio using Linear Regression

Aug 2016
2
0
DC
Hello, I have a question about linear regression modeling on ratio.

The original model with dependent variable of ratio is Y= (Y1/ Y2). Both Y1 and Y2 are dollar amount represent sales and balance respectively. The dependent variable Y is a continuous variable between 0 and 1.

The equation is Y=(Y1/Y2)=a+B1X1+B2X2. Basically this is a simple linear regression model.

My question is after I get the predicted Y by using the simple regression model, can I use the following equation to get the predicted Y1, the sales.

Y1=Y*Y2, where Y2 is the future estimated balance.

If this is correct, however, I see the predicted Y1 will eventually goes to 0, since Y2, the balance goes to 0 eventually. But Y1, the sales, can never goes to 0 in practical world. I am not sure where it goes wrong.

Thank you for your help.
 

romsek

MHF Helper
Nov 2013
6,837
3,079
California
your model doesn't make much sense as stated.

I don't know what balance refers to but if it goes to 0 eventually then Y likely becomes undefined.

Further if Y2, balance, tends towards 0, without a similar constraint on sales, then Y is not constrained to lie between 0 and 1 as stated.

Are you saying the relation between sales and balance is always such that the ratio lies between 0 and 1?

If this is the case then yes, as balance tends to 0, sales must also tend to zero, and must tend to zero faster than balance does, in order for the ratio Y to be defined.
 
Aug 2016
2
0
DC
Thank you very much. I have solved the problem. It is because certain values for Y1 or Y2 not be observed in my development data.