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what happens if my dependent variable is correlated with my time variable in a regression. I'm trying to add a time variable to control for trend but I notice that my dependent variable also increases over time.

Is it common or wrong to interact the time variable with your dependent variable?

How do I avoid spurious regression ( I'm not very knowledgeable on this I must admit)

Alice Work
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    Welcome to CV, Alice Work! Possibly of interest: De Boef, S. and Keele, L. (2008). [Taking time seriously](https://pdfs.semanticscholar.org/3a3e/d25148f942dc6038a1fb45bcb759575106a4.pdf). *American Journal of Political Science*, 52(1):184–200. – Alexis Dec 04 '18 at 04:22
  • @Alexis The reference does not address [spurious relationships](https://en.wikipedia.org/wiki/Spurious_relationship), which is not the same thing as the [regression dilution](https://en.wikipedia.org/wiki/Regression_dilution) arguments in the article linked to. Nice reference but off topic. – Carl Dec 04 '18 at 20:51
  • Possible duplicate of [What are some of the most common misconceptions about linear regression?](https://stats.stackexchange.com/questions/218156/what-are-some-of-the-most-common-misconceptions-about-linear-regression) – Carl Dec 04 '18 at 22:02
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    " *but* I notice that my dependent variable also increases over time." Why 'but', what is the problem with this? If you have (positive) correlation between some dependent variable and time then isn't this the case by definition. – Sextus Empiricus Dec 04 '18 at 23:13
  • What do you mean by 'interact'? – Sextus Empiricus Dec 04 '18 at 23:19
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    Did you mean to write independent variable the first or second time that you wrote dependent variable? – Sextus Empiricus Dec 04 '18 at 23:21
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    @Carl From the cited paper "Another important advantage of ECMs is that variables are parameterized in terms of changes, **helping us to avoid spurious findings** if the stationarity of the series is in question due to strongly autoregressive or near-integrated data, for example (De Boef 2001; De Boef and Granato 1997)." – Alexis Dec 05 '18 at 01:07
  • @Alexis No doubt. However, path length for discovering physics by *post hoc* analysis is a lot longer than insisting on *a priori* [balancing of units](https://en.wikipedia.org/wiki/Template:Classical_mechanics_SI_units). The difference in approach can be summarized as "I haven't the foggiest what is going on thus let me test an educated guess and come up with an MPU (minimum publishable unit)." VS "Let me systematize the problem and characterize everything with respect to deterministic causal factors, and conduct the experiment given an explicit set of assumptions to be tested." – Carl Dec 05 '18 at 01:24
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    @Carl The "path length for discovering physics" seems to be more or less irrelevant to the original question. – Alexis Dec 05 '18 at 16:45
  • @Alexis "Another important advantage of ECMs ..." is *post hoc* trial and error. That is not enough to balance units such that it is not efficient in helping us to avoid spurious findings. It may help, but is not rigorous. – Carl Dec 06 '18 at 02:32

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