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If I have a multiple regression like this $Y=a+b_1.X_1+b_2.X_2,$ how can I calculate the values of $b_1$ and $b_2$? I have searched on the web but couldn't find an answer.

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  • $\begingroup$ Generally look at the matrix notation for linear regression. Using linear algebra you can isolate the regression parameters. $\endgroup$
    – Chinny84
    Oct 22, 2014 at 19:34
  • $\begingroup$ Note we usually denote $a$ as $b_0$ $\endgroup$
    – Chinny84
    Oct 22, 2014 at 19:35

1 Answer 1

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Hint: rewrite $$ Y = \left( \begin{matrix} X_1& X_2& 1 \end{matrix}\right) \left( \begin{matrix} \beta_1\\ \beta_2 \\ a \end{matrix}\right) = X\beta $$and then apply the multidimensional linear regression results.

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  • $\begingroup$ So I should solve them just lika a set of linear equations? $\endgroup$ Oct 22, 2014 at 20:13
  • $\begingroup$ exactly. You have to solve $X^TX \beta = X^T Y$ for $\beta$. $\endgroup$
    – mookid
    Oct 22, 2014 at 20:21
  • $\begingroup$ Is the r-square value and RMS error for this case similar to how we calculate in single linear regression model i.e $\endgroup$ Oct 22, 2014 at 20:27
  • $\begingroup$ i.e r-square by calculating the 1-{sumof(yactual-ypredicted)^2/sumof(yactual-ymean)^2} $\endgroup$ Oct 22, 2014 at 20:29
  • $\begingroup$ yes, of course! this is just a vectorial formulation of the original problem. You can come back to the coefficients if you look at the coordinates of the solution! $\endgroup$
    – mookid
    Oct 22, 2014 at 20:33

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