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I have a OLS regression in the form:

$$Y_t=\alpha +\beta X_{t-1}+\varepsilon_{t}$$

Can I average out the constant during the OLS estimation/derivation and report,

$$y_t=\beta X_{t-1}+\varepsilon_{t}$$

Could I explain this as "I have averaged out the constant during the OLS procedure?"

So the intercept is there, the estimation procedure I use (code I have) averages it out, is there some correct technical jargon for this?

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    $\begingroup$ Did you mean centre the data before running the regression? $\endgroup$ – Huy Pham Dec 12 '18 at 11:59
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    $\begingroup$ Yes, I did!!!!!!!!!!!!!!! $\endgroup$ – user22485 Dec 12 '18 at 12:02
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    $\begingroup$ See the third answer in stats.stackexchange.com/questions/201919/… $\endgroup$ – Christoph Hanck Dec 12 '18 at 12:30
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    $\begingroup$ @ZarinaAkhtar so i mean, unless I'm missing something, that's what it's called. You mean centred the data so the intercept=0. Your residuals should still be ok. $\endgroup$ – Huy Pham Dec 12 '18 at 13:30

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