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How do you call a regression such as :

$ Y_{i} = \alpha _{i}+ \beta _{i} \times X_{i}$ where $\beta _{i}$ is changing for each $_{i}$ ?

Thanks for your help

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  • $\begingroup$ What does $i$ index? Is it datapoints, or variables/dimensions? $\endgroup$
    – user20160
    Jul 21, 2018 at 23:44
  • $\begingroup$ This is single variate linear regression without the error term. $\endgroup$
    – Chris
    Jul 21, 2018 at 23:50
  • $\begingroup$ @user20160, it is datapoints. $\endgroup$
    – bixoez
    Jul 22, 2018 at 0:01
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    $\begingroup$ @chris : i know it's just an equation, i'm trying to put some words on it in order to find a methodology to implement in r .... $\endgroup$
    – bixoez
    Jul 22, 2018 at 1:10
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    $\begingroup$ If you only have one y for each $i$ the system of equations won't be identifiable unless you relate the coefficients over time. $\endgroup$
    – Glen_b
    Jul 22, 2018 at 11:27

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