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When I run a linear regression in the form of $y$ = $\hat{β}_0$ + $\hat{β}_1x$, I not only can calculate the values and SE of $\hat{β}_0$ and $\hat{β}_1$, but also their z-scores. Now what I don't understand is how can we know their z-scores if we don't know the true coefficients in the population (i.e. $β_0$ and $β_1$)? I thought the whole point of a regression is to estimate them?

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user352112
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  • The null hypothesis for the t-test is that the coefficients are equal to 0. This might not be a meaningful hypothesis to test, esp. for the intercept. And the regression did estimate the parameters. For example, the confidence interval for the educ (education?) coefficient is [89, 144]. – dipetkov Mar 17 '22 at 00:53
  • Just to be perfectly clear: the z-scores in this output compare the estimates to zero, not to the true values. – whuber Mar 17 '22 at 15:34

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