One tool is the so called Granger causality:

http://en.wikipedia.org/wiki/Granger_causality

http://www.scholarpedia.org/article/Granger_causality

Are there any other informations about your X & Y variables?

I hope, this paper can be a guide to you:

Urquhart, N. S. The anatomy of a study. Hortscience. 16(5): 1-5, 1981.

Best regards

jwalter

Granger causality might be relevant if the variables are time series, otherwise not. A theory is a prerequisite for determining the causal relationship in my opinion.

One way to find out the independent and dependent variables is go through the standard cointegration tests and then tests of Granger-causality through the vector error-correction model, then variance decompositions and impulse response function analyses. The results can then be used for important policy formulations.

Thanks.

Best wishes,

Mansur Masih

Causality is determined only through an experimental design. In the design the independent variable is identified prior to the conduct of the study.

In ex post facto designs, causality cannot be established, but relationship can be, in such case, the identification of which one is independent (explanatory) or which is dependent, may depend on logic, on existing theories, on related studies, or the hypothesis formulated.

Thank you for your reply everyone. 

@Demetris, X and Y are not time series. I can not use Granger Causality here I suppose.

Now what can I use?

You have to give us some more details dear friend...

All what I have is this: X and Y are two continuous variables, they are not time series. they have correlation between them (around 0.7).

As Eddie says Causality is normally determined only through an experimental design. In the design the independent variable is identified prior to the conduct of the study.

If dependence/independence not known have you considered co-dependence/interdependence? If you assume there may be  relationship can be, in such case, the identification of which one is independent (explanatory) or which is dependent, again as Eddie outlines, this may depend on logic, on existing theories, on related studies, or the hypothesis formulated, however many use the tests of Wiener-Granger causality to establish  but this is mainly used if one of your variables is time - you need to supply more information on your variables. Go see:

Bressler and Seth (2011) in Neuroimage Jnl.

http://www.sciencedirect.com/science/article/pii/S1053811910002272

.

there have been extensive discussions on this "causality" topic in this RG thread

https://www.researchgate.net/post/Cause-effect_dilemma2

.

@Robert and Eddie. An experiment is a good way to acertain the causual effect of one or several variables on the response variable. However, prior to designing the experiment one needs to have an idea about the purported causal direction between the variables. And this is the original question. This direction can only be identified by relying on a theory, I think. 

With so few available infos, personally, I don't suggest a solution.

Imagine you have observed a correlation like y = 2x. If you solve the equation for x it results: x = y/2 .

So as mentioned above, you have to know the original problem.

From my point of view a previous theory is usually advisable, but not essential. What is really indispensable to study causality (at least n your case) is conducting an experiment, i.e., to manipulate a variable (iv) and analize the effects on the other (dv). Nevertheless, before the experiment, as Kenneth suggest, you should asking yourself about the main question that will guide it. This essential first question may arise from previous theories and/or from former results and/or from your own intuition (or ideas), etc. In any case, this initial question have to be operationalized in general and specific objectives and in an specific hypothesis (or maybe several), that may or may not be directional. In sum, you just need the aforementioned essencial question and idea: the rest it should be a (hard-earned) piece of cake. Good luck!

The Independent Variable causes a change in the Dependent Variable.

Regression is not necessarily cause and effect. The Y variable is considered to be a random variable, because it includes a random variable. The x variable, or variables, is/are used to formulate the predicted-y-values. We "predict," meaning "estimate" when what is being estimated is a random variable, using x-values, which are generally static values with no random component. Sometimes x-values are considered to have a measurement error, and each case may be measured multiple times and an average used. A colleague even used another regression to impute for some x-values, but the random component would then pass through mathematically to adhere to the y-value. So in the linear regression here, we always have Yi predicted by a linear 'formula' of x-values, and Yi is then equal to the predicted-yi plus a random "error," which is not really an error, but a random variable with zero expectation.

You can have a situation where x causes Y, and it would be written like a regression, but the regression discussed here would just mean that x is a predictor for Y. Prediction does not necessarily mean causation.

The question asked which of two variables in a simple linear regression should be an "independent" variable, and which should be the dependent variable. You use x for the former when you want to use that to predict for Y, the latter. ("Independent" is not a really good term here because when you have more than one, they do work together, and influence each other. A common concern is 'collinearity,' meaning the information contained in one predictor or set of predictors overlaps with another predictor or set of predictors.)

I heard an interesting example once which would be prediction, but not causation: Drinking sports drinks is a good predictor for knee injuries, but not a cause. People who drink sports drinks may often participate in sports, where they may suffer knee injuries. (I guess you could do a logistic regression for this. Not my area.)

I suppose that often you will know that you only have prediction, and often you may just suspect causation.

In official statistics one often has an infrequent census, perhaps annually, and a more frequent sample, say monthly, on the same variables/items. The same item on the census survey can be used as a predictor for that item on a later sample survey. Then x predicts Y but does not cause it. In fact, there are "births" and "deaths" for such survey work, notably with establishment surveys, and for a "death," an establishment may cease operation, and the y-value become zero, when a large value might otherwise be predicted. The x will then certainly not have any ability to cause Y.

This absurd "problem" exists only because the traditional regression wants to treat the variables differently! It is completely nonexistent if you use multidirectional regression! Try it for free: www.lerenisplezant.be/fitting.htm.

Not a problem. One is a random variable. The other (or others) is (are) not.

The dependent variable is the random variable. Look it up.

Random variables are the basis for regression models, as opposed to deterministic models. 

James R Knaub That's exactly my point: what you call a "random variable" (I absolutely don't like this expression) is a CHOICE. If you measure the voltage over and the current through a resistor, you choose one as the "independent" and the other as dependent. The same for pressure & temperature of a gas, or height & mass of a person, etc. There is absolutely no objective reason for that choice. The traditional least squares method assumes that x is "perfect" without measurement error or other uncertainty, and only y is "imperfect". This is complete nonsense since there is no such thing as an infinitely precise measurement. This choice influences the value of the parameters, sometimes dramatically! In my multidirectional regression, x and y are treated equally and you get the same results, no matter the choice you make. I was raised with the idea that conservation of symmetry is very important in physics...

The only kinds of situations that come into my mind with a clear "independent" variable, are time series with e.g. economic data, where the time variable is not "causing" the y data; or not-invertible relationships like spectral data.

A deterministic model does not have random "error."

Measurement error and "random error" are not synonymous.

James R Knaub I just mean all the uncertainty on measurements. I don't know how it is in your world, but I have always learned that measurements can have "random" (ideally gaussian) and "systematic" errors.

Consider one year's corn crop as a predictor for next year's corn crop. Obtain data by farm. A ratio model is appropriate. The slope would be the "growth" rate (where less than 1 is a decrease from one year to the next). If you plot these data, you don't have to have all of the current year's data. You can "predict" for missing data.

Here is the important part here: The residuals are not measurement errors. The dependent variable (new year's production of corn) is not caused by the independent variable (last year's production of corn). But bx does "predict" (estimate) for y:

Yi = bxi + ei.

"Measurement error and 'random error' are not synonymous."

Estimated residuals are not synonymous with measurement errors.

- Please see all of my responses above.

Well, correlation does not implies causality. Even more, there are well known spurious correlations (https://www.datasciencecentral.com/spurious-correlations-15-examples/). Always it is needed a broad view of a problem to assess some correlation.

James R Knaub Yes, but can you please reply to my arguements?

To predict crop yields from one harvest, you don't need regression, you can only guess that it will be more or less the same. If you measure the yields in many years toghether with temperature and rainfall data, we can start doing regression.

Koen Van de Moortel -

I have replied, but you do not seem to be talking about regression. Consider a book on regression such as the following.

Weisberg, S.(2014), Applied Linear Regression, 4th ed., John Wiley & Sons

You seem to be thinking deterministically. I can only suggest you re-read my notes above.

Best wishes. - Jim

James R Knaub Please man, don't treat me like I don't know anything about regression. I have decades of experience with it. You did NOT answer to the point I made about the artificial distinction between "dependent" and "independent" variables. I bet you can not find any flaw in my reasoning.

Of course regression (in real natural science at least) is about "deterministic" relationships! In non-chaotic circumstances there IS a (macroscopic) deterministic relationship between things like current and voltage etc. Regression allows us to find the parameters that best fit with reality, and the error margins for those parameters.

You seem to think only about exploratory "science", in which they use mostly linear regression because they have no clue what is really behind the observations.

Koen Van de Moortel - As I said, an estimated residual is not synonymous with a measurement error. Since you do not recognize the legitimacy of the term "random variable," sorry, but there is nothing for us to talk about.

James R Knaub I'm educated in physics. We don't speak about "random variables" there. But that doesn't mean I'm not right about the point I am making. I am trying to show you I know how to make better bread, and your only answer is "yes but you can't make pastry".

I've had substantial physics as well. You are off topic. This thread is about regression, not correlation. This has become counterproductive. I am done responding.

James R Knaub What are you talking about? Regression is one of the possible tools to detect a correlation, and that is the topic here. I don't understand why you want to fight instead of answering to my point. We are all here to learn something, by dialog!

Hello to anyone who has gotten this far,

As an observation, folks should be aware that both the concept of and need for random variables are genuine, and central to a slew of statistical methods.

As a second observation, a correlation is nondirectional with respect to two score sets (e.g., r for (x,y) pairs is exactly the same as r for (y,x) pairs). (Please note: this is not to say that a correlation cannot be signed, as to represent the slope of the best fitting linear function linking the two.)

As a final observation, it seems to me that the original query for this thread brings up two salient points:

1. Correlation is insufficient for asserting a causal relationship. (Point made in Eddie Seva See's reply); and

2. You can run a regression with two sets of scores, or fit either or both sets to some specific function (curve-fitting), but in either instance, the choice of the object score should always be driven by the specific research question, hypothesis, or relevant theory under investigation (Point made in Kenneth Carling's reply).

And, if Irshad Samdani Mujawar is still paying attention to this thread:

Good luck with your work.

A way of identifing the Independent Variable (IV) and the Dependent Variable (DV) in an experiment is by checking which causes the change .i.e The IV causes a change in the DV. It is not possible that DV could cause any change in IV.

The predictor (IV) may not actually cause the response. Causation is not required. The predictor provides the fixed (except for possible measurement error in errors-in-variables models) values, and we see what response we find from using such a value for the predictor, where the response also includes an estimated residual (estimated because we do not have an 'exact' model). So the response variable (DV) is a random variable because e is an estimate for epsilon, which is a random variable. So we have a distribution of values for Y to go with a value for x. But x may only be correlated with Y, not the cause of it.

An independent variable is what is not affected by any change that is it is stand-alone but the dependent variable is usually affected by a change.

https://www.scribbr.com/methodology/independent-and-dependent-variables/