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Why the writer use the minus the average of x in the x matrix?

matrix form

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  • $\begingroup$ That will give for example $y_n=\gamma_0 + \gamma_1(x_n-\bar x) +\varepsilon_n$. If you compare it to $y_n=\beta_0 + \beta_1 x_n +\varepsilon_n$ then you would get $\beta_1=\gamma_1$ and $\beta_0 = \gamma_0 - \gamma_1 \bar x$, so the issue is whether the intercept is measured at $x=0$ or $x=\bar x$. Remember that the OLS regression line passes through the mean of the data $\endgroup$
    – Henry
    Jun 25, 2021 at 8:12
  • $\begingroup$ Thanks for your nice answer. :) So we have two notations of one thing and it depends on your problem. Please give me a link to study more if it is possible. also for OLS. $\endgroup$ Jun 25, 2021 at 8:21
  • $\begingroup$ @Henry maybe convert it into an answer. $\endgroup$
    – Tim
    Jun 25, 2021 at 8:24

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As requested in comments:

That will give for example $y_n=\gamma_0 + \gamma_1(x_n-\bar x) +\varepsilon_n$.

If you compare it to $y_n=\beta_0 + \beta_1 x_n +\varepsilon_n$ then you would get $\beta_1=\gamma_1$ and $\beta_0=\gamma_0 - \gamma_1 \bar x$,

so the issue is whether the intercept is measured at $x=0$ or $x=\bar x$.

Remember that the OLS regression line passes through the mean of the data.

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