# Correlation of three values

I have a data set that considers three values, $x,y,z$. And I have three questions:

1. What's the relationship between $x$ and $y$?
2. What's the relationship between $z$ and $y$?
3. 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.

• Oh! I see. Btw, $x,y$ and $z$, are discrete, I assume the formula $y=\beta_0+\beta_1x+\beta_2z+\epsilon$ doesn't changes. Also, where can I find examples with three values, because the book that I'm following considers two values, and I'm not sure what to do. – Ana Galois Jan 24 '16 at 19:28
• Are you assuming that your sample of $x$ and $y$ came from discrete variables? Regarding the examples - any standard book on regression analysis will provide plenty examples of that kind. – V. Vancak Jan 24 '16 at 21:14
• Oh, don't mind that, I got confused with another word. Thank you. – Ana Galois Jan 25 '16 at 17:56