{'fraction_non_alphanumeric': 0.02666666666666667, 'fraction_numerical': 0.015238095238095238, 'mean_word_length': 5.493827160493828, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
When Does the Ecological Fallacy Vanish in Linear Regressions?

As regards regressions, the ecological fallacy suggests that coefficients obtained from aggregate (or group) data often differ from those of the same statistical model and data at the individual level. Comparing the linear regression frameworks of Firebaugh (1978) and Piantadosi et al. (1988), this paper shows that the ecological fallacy vanishes when group effects, due to which the statistical relationship could depend on the group environment, are absent.