As a student learning Applied Regression Analysis, I come from a background with very little information about this topic.
I understand that given $y = \beta_0 + \beta_1x_1 + \epsilon$
$E(y\mid x) = \beta_0 + \beta_1x_1$ is an exact linear relationship.
However, if we use a function as log($x$), sin($x$), or cos($x$), will the relationship continue to be linear?
For instance, in the parameters $\beta$,
$E(Y\mid x_1,x_2) = \beta_1 x_1 + \beta_2 \log(x_2)$, is this linear?
Clearly, $\beta_1x_1$ is linear; however, is the part $\beta_2\log(x_2)$ also linear? From a calculus point of view, we know that the logarithm function isn't exactly linear in the sense it is a polynomial of degree one.
Any hints are much appreciated.