# Correlation , Regression and Causal inference

Based on several posts i read on stack exchange I now know that neither correlation nor regression indicate causation,

then why is it said that the 2 main uses of regression are 1)prediction 2)causal analysis and inference ??

Reference to the following article by Dr Paul Allison

http://statisticalhorizons.com/prediction-vs-causation-in-regression-analysis

In a causal analysis, the independent variables are regarded as causes of the dependent variable. The aim of the study is to determine whether a particular independent variable really affects the dependent variable, and to estimate the magnitude of that effect, if any.”

If your knowledge about the world teaches you, that a dependence should be in one direction (maybe because you have experimental data where you changed one parameter willingly), then regression is a worthy tool to investigate that relationship more closely. Therefor it is used in the investigation of a relationship, but in itself it cannot decide on the direction of causality. Pure observation cannot do that, experiments can do that. The mathematics of regression is the same in both cases.

• So , we must have experimental data with independent variables that have already been proven to establish a causal relationship in one direction only to be later validated by regression? – Narayanan Feb 8 '17 at 10:28
• If you observe A and B and both correlate, then you don't know, whether A influences B oder B influences A or both are influenced by a common C. Neither correlation nor regression can answer that. If, in an experiment, you change A and B follows, that is proof of a causation "A influences B". The difference is not in the math but in your knowledge about how the data came to be. – Bernhard Feb 8 '17 at 10:39
• True. What happens in case we are interested in multiple regression and each of the independent variables have been earlier 'known' to have a positive or negative correlation with the dependent. Shall i look at the overall R square and F value and signs of the coefficients and individual p values to eliminate those with a p value<0.05 and draw conclusions validating/invalidating the causation ? – Narayanan Feb 13 '17 at 2:06
• Also the term direction the way ive understood it is the positive/negative correlation. Example : Translating it into simple regression the equation for a negative correlation could be like this y = 6.789 - 25.6 X. But what about multiple regression - Does negative correlation mean a negative sign of the individual co-efficient ? – Narayanan Feb 13 '17 at 2:20
• A correlation has a direction and a causation often has a direction and these are different things. Deleting predictors because their p-value is >.05 may or may not be a good idea depending on what purpose the regression was computed for. And yes, the sign of the individual coefficient gives the direction of the influence of any predictor within this particular model. – Bernhard Feb 13 '17 at 15:13

Adding to @Bernhard 's answer, perhaps an example would help. Suppose we are interested in the relationship between height and weight in adult human males.

Statistically, we could use either height or weight as the dependent variable. The computer doesn't care. But it only makes sense to use weight as the DV. That "sense" comes from us and our knowledge of how people are, how we grow and so on and also from the notion that weight is more changeable than height.

We can sometimes rule out one direction of causation: It can't be that cancer causes smoking, if cancer happens later in time. (But that, alone, doesn't mean that the correlation between smoking and cancer implies causation).

More generally, we should not separate the statistics from the rest of the argument we are making. When we analyze data, we need to understand the data.

• Thank you sir for that answer. I've commented on bernhards answer. kindly have a look, – Narayanan Feb 13 '17 at 2:07