# OLS parameter estimation of an expression?

During my research for a class, I came across a paper that said they estimated an equation using OLS. But the parameter they were estimating appeared to be an expression that looked like this (not the actual equation just something I made up to illustrate):

$$y = \frac{\beta-1}{2}\chi$$

Rather than what I am used to seeing for OLS:

$$y = \beta_{0}X_{0} + \beta_{1}X_{1}$$

How does one estimated the equation that way? Or am I missing something?

• Could it be that they estimated the expression in front of $X$ as a whole by OLS and then obtained $\beta$ by multiplying the obtained value by two and adding one? – Richard Hardy Feb 25 '15 at 6:58
• It would be impossible to tell without a reference or a description of what $\chi$ here is. – StatsStudent Feb 25 '15 at 7:09
• What was the paper? – Glen_b Feb 25 '15 at 10:25

As Richard Hardy said in his comment, in this case you can simply estimate $y=\delta X + \epsilon$. Since $\delta = \frac{\beta - 1}{2}$, you can calculate $\beta = 2\delta + 1$. You do this kind of thing when your regression equation comes from a theoretical model.