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I know that there are similar questions but I hope this is not a duplicate, unfortunately I can't tell due to my limited knowledge about statistics..

I have annual data covering a period of 100 years (one predictor and one dependent variable). I'd like to investigate the relationship for the years 1-50 and for the years 51-100, so I fit a linear regression for each period. However, I'd also like to know if there is a significant difference between those two models (i.e. determine whether it makes sense to split the dataset). What test would I use for that?

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The Chow test is used for testing whether a structural break is present in a time series. Most software packages have this test available.

Chow, Gregory C. (1960). "Tests of Equality Between Sets of Coefficients in Two Linear Regressions". Econometrica 28 (3): 591–605. doi:10.2307/1910133

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