Regression on a constant If I have observations of $y_{i}$ and $x_{i}$ which are i.i.d. I also have OLS assumptions such as $E(\epsilon_{i} \mid X_{i})= 0$, my qustion is:
If I project $y_{i}$ onto a constant $\mu$, that is, we have model
$y_{i} = \mu + \epsilon_{i}$. Does finding the OLS estimator $\hat\mu$ has anything to do with $x_{i}$? Because in my opinions, $x_{i}$ never emerges.
Thanks~
So basically the question is: 
If I know the average ($\hat{\mu}$) of the daily temperatures ($y_i$) of last year, does that tell me anything about how many people were born ($x_i$) each day?

Unsurprisingly the answer is no.

The most you can get is the average of the $x_i$ series if you have the parameters of an unbiased regression between $x_i$ and $y_i$.