These terms kind of confuse me because they all seem to imply a certain correlation.

Confounder: influences dependent and independent variable

Collinearity: to me just means correlation between indepedent variables

Interaction term: joint effect of independent variables (but doesn't this require correlation between those variables?)


1 Answer 1


Your understanding of confounding and collinearity is correct. Note that in many contexts collinearity really refers to "perfect collinearity" where one variable is a linear combination of one or more other variables, but in some contexts it just refers to "high correlation" between variables.

Of course, in order for confounding to occur, there has to be a degree of correlation, though I would avoid saying "collinearity" due to the above.


interaction term: joint effect of independent variables (but doesn't this require correlation between those variables?)

A "joint effect" is a good way to undersdand it, but in no way does it require correlation between the variables. Consider an orthogonal factorial design experiment for example.

As another example we could also show this with a simple simulation of bivariate data where X1 and X2 are uncorrelated yet a meaningful interaction exists:

> set.seed(1)
> N <- 100
> X1 <- rnorm(N)
> X2 <- rnorm(N)
> cor(X1, X2)
[1] -0.0009943199   # X1 and X2 are uncorrelated
> Y <- X1 * X2 + rnorm(N)
> lm(Y ~ X1 * X2) %>% summary()

lm(formula = Y ~ X1 * X2)

     Min       1Q   Median       3Q      Max 
-2.92554 -0.43139  0.00249  0.65651  2.60188 

            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.03107    0.10439   0.298    0.767    
X1          -0.03352    0.12064  -0.278    0.782    
X2          -0.02822    0.10970  -0.257    0.798    
X1:X2        0.76032    0.14847   5.121 1.57e-06 ***
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    $\begingroup$ Does this answer your question ? If so, please consider marking it as the accepted answer, and if not please let us know why. $\endgroup$ Commented Aug 21, 2020 at 12:06
  • $\begingroup$ If based on linear regression you find that age has an effect on a physiological parameter. You want to use that parameter to predict the existence of a disease. Is age a confounder that should be accounted for in the prediction or a parameter that should be excluded from the analysis to avoid multicolinearoty issues with the physiological parameter? $\endgroup$
    – Sapiens
    Commented Apr 20, 2021 at 6:55

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