In simple linear regression, does the variable x represent the stochastic component, while the coefficient b represents the determination?
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https://stats.stackexchange.com/questions/215230/what-are-the-differences-between-stochastic-and-fixed-regressors-in-linear-regre/417324#417324 – kjetil b halvorsen Oct 26 '23 at 20:12
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In general, $x$, in a bivariate rgeressions of the form $y=a+bx+u$, is called the explanatory variable and is considered to be a random variable. $u$ is the unobserved component, which is also random. $a$ and $b$ are model parameters, where $b$ is often focused on in most studies since it can quantify the effect of $x$ on $y$.
Math-fun
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Can you edit to clarify what should come before is called the explanatory variable ? – kjetil b halvorsen Oct 26 '23 at 20:11
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Thanks a lot for the comment :-). I just edited the sentence. It was a indeed not a smooth senetence before. – Math-fun Oct 27 '23 at 13:59
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No. In a simple linear regression: $y = b_0 + b_1X + e$, the regressor (x) may be stochastic or not; the coefficient ($b_1$) is the size of the effect. However, the error term is (AFAIK) always stochastic.
Peter Flom
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