# Thread: Model Ratio using Linear Regression

1. ## Model Ratio using Linear Regression

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.

2. ## Re: Model Ratio using Linear Regression

Note, linear regression requires the assumption of unbounded DV, whereas in your case the ratio is bounded between 0 and 1. As such, your estimates might be biased. To address this issue, you can explore beta regression or glm fractional logit. Now, answering your question, calculating Y1 does not seem plausible to me.

3. ## Re: Model Ratio using Linear Regression

kiton,

You live in a corn field, I love it. We will hope sweet corn and not feed corn.

Second, I had not heard of fractional logit. Do you have any more information before I check the web?

Thanks!

P.S., I just found this:

http://support.sas.com/resources/pap.../1304-2014.pdf

4. ## Re: Model Ratio using Linear Regression

Still not sure these approaches get at your question. You could always say such in such ratio to solve for Y1, but certain values for your Y1 or Y2 may not be observed in your data, so they may not be identifiable or possible for extrapolation???

5. ## Re: Model Ratio using Linear Regression

Thank you very much for all of you. I have solved the problem. It is because certain values for Y1 or Y2 not be observed in my data.

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