Computer-implemented systems and methods for robust confidence interval analysis

A non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by a computer, cause the computer to:

• read, a dataset representative of a plurality of distribution agnostic measurements, the dataset comprising a plurality of observations, wherein each observation comprises a response variable value and a plurality of explanatory variable values;
• fit, a regression solver to the dataset to express the response variable value as a function of the plurality of explanatory variables;
• compute, a sample coefficient of multiple determination based on the function;
• compute, a kurtosis of a sample of fitted values;
• and
• output, a one- or two-sided confidence interval for a population coefficient of multiple determination.

A computer system comprising:

• a processor;
• and
• a memory storing instructions that, when executed by the processor, configure the computer system to:
• read, a dataset representative of a plurality of distribution agnostic measurements, the dataset comprising a plurality of observations, wherein each observation comprises a response variable value and a plurality of explanatory variable values;
• fit a regression solver to the dataset to express the response variable value as a function of the plurality of explanatory variables;
• compute a sample coefficient of multiple determination based on the function;
• compute a kurtosis of a sample of fitted values;
• output a one- or two-sided confidence interval for the population coefficient of multiple determination.