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I have read that in regression there is no need for the response variable (independent variable) to be statistically independent. The source is https://en.wikipedia.org/wiki/Multinomial_logistic_regression, under assumptions: "As with other types of regression, there is no need for the independent variables to be statistically independent".

I understand what it means to be statistically independent, but I cannot think of examples of when the response variable would/ would not be statistically independent.

Could you give an example of a statistically dependent response variable vs. a statistically independent response variable?

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  • $\begingroup$ Could you please post a reference where you have seen this? "Independence" requires multiple variables to be discussed. $\endgroup$
    – Dave
    Commented Jun 18, 2021 at 13:56
  • $\begingroup$ $y_t = f(y_{t-1}) + \varepsilon_{t}$? Conditions today are a function of conditions yesterday? $\endgroup$
    – Alexis
    Commented Jun 18, 2021 at 14:44

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Example of independent response: Exam results are recorded for a class of 30 students. We might use a t-test, or a linear regression model for such data.

Example of non-independent response: Exam results are recorded for students in several classes. Results for students in one class are more likely to be similar to each other than results for students in other classes, perhaps due to different teachers. To account for this non-independence, we might use a linear mixed effects model, or use a linear regression model with fixed effects for the class identifier.

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  • $\begingroup$ Does this answer your question ? If so please consider marking it as the accepted answer. If not, please let us know why. Also, if you haven't already, please consider upvoting it. $\endgroup$
    – Robert Long
    Commented Jun 26, 2021 at 12:22

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