TITLE: Inverse Sampling of Degenerate Datasets from a Linear Regression Line 

ABSTRACT: When linear regression generates a relationship between a (dependent) scalar
response and one or multiple independent variables, various datasets providing
distinct graphical trends can develop resembling relationships based on the
same statistical properties. Advanced statistical approaches, such as neural
networks and machine learning methods, are of great necessity to process,
characterize, and analyze these degenerate datasets. On the other hand, the
accurate creation of purposedly degenerate datasets is essential to test new
models in the research and education of applied statistics. In this light, the
present study characterizes the famous Anscombe datasets and provides a general
algorithm for creating multiple paired datasets of identical statistical
properties.
When linear regression generates a relationship between a (dependent) scalar
response and one or multiple independent variables, various datasets providing
distinct graphical trends can develop resembling relationships based on the
same statistical properties. Advanced statistical approaches, such as neural
networks and machine learning methods, are of great necessity to process,
characterize, and analyze these degenerate datasets. On the other hand, the
accurate creation of purposedly degenerate datasets is essential to test new
models in the research and education of applied statistics. In this light, the
present study characterizes the famous Anscombe datasets and provides a general
algorithm for creating multiple paired datasets of identical statistical
properties.
Inverse Sampling of Degenerate Datasets from a Linear Regression Line
http://arxiv.org/abs/2108.11477v1