Let's say, I have:
$y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3$
I fit a multiple linear regression (MLR) model (
lm() command) in R, and see a very large $p$-value for $\beta_1$ (say 0.5). Now, if I leave out $x_1$ and fit another model:
$y = \beta_0 + \beta_2 x_2 + \beta_3 x_3$
I see $\beta_2$ and $\beta_3$, and consequently, their significance change. I'm thinking it should make more sense to fit the second one and the first one is probably faulty, because of an insignificant effect in the model. So if I want to see if there is really a linear relationship between $x_2$ or $x_3$ and $y$, I should leave the other variable out, right?