I have a data set that considers three values, $x,y,z$. And I have three questions:
- What's the relationship between $x$ and $y$?
- What's the relationship between $z$ and $y$?
- What's the relationship between $x$ and $y$ controled by $z$?*
For the first two questions I did pretty much the same thing, I made an scatterd graph and saw that they hold a positive and negative correlation. I don't know if I should do more... what else can I show? I mean, knowing if it is a positive or negative correlation already answers the questions, right?
On the other hand I'm not completely sure what controled by means. I belive it sounds like a condition, but I'm not sure what to do here.
* in spanish the question is: ¿Cuál es la relación entre $x$ y $y$ controlado por $z$?
3) Assuming that $y$ and $x$ are continuous, you probably expected to estimate the regression model $$ y = \beta_0 + \beta_1x + \beta_2z + \epsilon, $$ and report the $\beta_1$ with its standard error, while "controlling" for $z$, i.e., (probably), by estimating the model you are addressing the effect of $x$ on $y$ in the presence of $z$. And when interpreting $\beta_1$ you assume that you do it ceteris paribus, namely, $z$ is hold constant.