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?
Shifat -
Is your 'target' variable a response variable, and you want to see if the other variables could be predictor variables as in multiple regression? If you have continuous data, graphing these relationships becomes very helpful. You can see how each individual "input"/predictor variable relates to the "target"/response variable individually, and even use regression at that level, but please note that when the predictors are used together, they generally have impact on one another, perhaps most notably collinearity, and the relationships change, but you can look at the overall predicted-y by using a "graphical residual analysis." A graphical residual analysis even works if some quantitative predictor variables are not continuous. (A "cross-validation" can be used to study whether you have fitted too closely to that one particular sample.)
Plotting continuous variables against each other can be informative.
I'm not certain that I addressed your actual question. If not, perhaps you could clarify.
Cheers - Jim
Dear Hossain,
I suggest in the same line as the colleague, but if the target and variables have multiple influences, you could apply network analysis. This is a robust analysis. It is important to notice that network analysis is not social network analysis; it is another thing. You can conduct it using R.
But as the colleague, I'm not sure if I answered your question.
Regards,
Amalia
James R Knaub and Amalia Raquel Pérez Nebra , thank you for your answers and at the same time, I am very sorry for not being clear at the time of asking the question.
I will definitely study what you suggested in your answers. I have modified the question to be more specific to my goal.
I am not sure if I understood the initial question correctly and if it is all about the correlation of 3 variables, but what immediately came into my mind was that Peason correlation only quantifies the "linear" relationship . Maybe another correlation would be more informative for your data/functions: the distance correlation
https://en.wikipedia.org/wiki/Distance_correlation
Quote from wikipedia:"The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors."
Maybe this helps.
Best,
Rainer
Rainer Duesing thank you for your answer. Actually the data I showed here is a fabricated dataset, only for an example. In this case we know that the target variable r is related to x and y with distance function and not related to variable z.
But if we did not know the exact relation among the target and input variables, is it possible to analyze if some of the input variables are related to the target and can be represented by a function f(inputs) = target?
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