If for example, I have a large enough dataset with multiple input variables and one target. But it is unknown whether the input variable(s) are correlated with the target or not. Is there any way to quantitatively analyze if the target has a correlation with the input variable(s) only from the data points?
For example, I have three independent variables x,y, and z. And dependent variable (target) is r. Here for the purpose of demonstration, the (x,y) is known to be (m*cos(m)/c,m*sin(m)/c). This is a function of a spiral in a 2D space, where the m is an array of points and c is a constant. (Figure is attached) The target variable r is the distance of the (x,y) points from the origin (0,0) in the 2D cartesian space.
The independent variable z is said to have uniform random values and has no relation with the target variable r.
The values of the Pearson's r for an independent variable and the target are found to be
r_x,r = 0.03250883308649153
r_y,r = -0.10980064148604964
r_z,r = -0.17896621141606622
Now to be specific, my question becomes is there any quantitative way to observe that the x and y variables together have a correlation to the target variable, and variable z has no correlation with the target r?