Deconstructing the Friday the 13th Effect: Evidence from Dummy-Variable Regression, Wavelet Analysis, and XGBoost Prediction

Abstract

Starting from the question “Is Friday the 13th superstition or fact?”, this paper constructs a comprehensive evaluation framework from statistical falsification, signal deconstruction, to intelligent prediction, and discusses whether “Friday the 13th” is supported by realistic evidence, as well as whether the personal well-being of the public is affected by superstitious date characteristics.For Task 1, we first established a multiple linear regression model with dummy variables (Task 1.1). Through the deconstruction of date attributes, it was found that both the regression coefficient of the “Friday the 13th” variable and the p-value of the one-way analysis of variance were far greater than the significance level. They were statistically insignificant, directly falsifying the special negative effect of “Friday the 13th” at the empirical evidence level. Subsequently, we constructed a dummy-variable regression model with multiple-comparison validation (Task 1.2), and conducted sensitivity analysis by combining the consistency test of residual performance across different regression methods, proving the robustness of the non-significant conclusion. It was also found that, when independence was controlled, the effects of different dates and cycles remained insignificant. To further explore the deeper characteristics of the time series, we used multi-scale wavelet analysis (Task 1.3) to perform time-frequency deconstruction of event frequency based on frequency and significance. The results show that risk energy is mainly concentrated in macro long-wave cycles, such as policy cycles or pandemic cycles, while specific date numbers only appear as random high-frequency noise. This indicates that, from the perspective of the financial market, there is no such thing as a “good day” or a “bad day.”For Task 2, we constructed a multi-dimensional evaluation indicator system to measure the happiness index from five dimensions: the atmosphere of social public opinion, public health safety, social harmony and stability, climate change, and economic conditions, and used the Kendall correlation coefficient for heterogeneity validation. We then used the Entropy Weighting Method to determine the relative importance of each indicator. The results show that pandemic-related and environmental indicators (PM10) account for the highest proportion of influence on individual well-being. We then conducted a reliability analysis of the weight distribution in combination with practical reality. On the whole, the weight setting is consistent with realistic evidence.For Task 3, we used the XGBoost gradient boosting method to establish a risk prediction model. By analyzing various data features, the model can identify signals with real early-warning significance. The empirical research shows that the prediction performance based on physical environmental indicators is far better than the traditional superstitious prediction based on date numbers, providing rational risk early-warning rules for the public. At the same time, the prediction of “good days” and “bad days” largely depends on the updating of real-time information.The conclusion shows that social risks are driven by institutionalized cycles and physical environmental variables, rather than date superstition. This model not only provides the public with a rational quantitative tool, but also provides a robust mathematical paradigm for dealing with heterogeneous social events.