Study on Linear Correlation Coefficient and Nonlinear Correlation Coefficient in Mathematical Statistics
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Bibliographic record
Abstract
In the two-dimensional or multidimensional experimental data in the traditional statistics, there is usually a linear relationship, or a similar linear relationship between independent variables and the dependent variable. Commonly the linear correlation coefficient is used to measure the degree of linear between the independent variables and the dependent variable. However, for the two-dimensional or multidimensional experimental data, there may be a simple linear relationship between independent variables and the dependent variable, or a simple non-linear relationship, or both linear and non-linear relationship. Article [1] found that the traditional correlation coefficient (linear correlation coefficient) r is only suitable for simple linear relationship. On the basis of article [1] , this article discusses the linear correlation coefficient r , analyzes nonlinear correlation coefficient r nl , and gives a new definition of the correlation coefficient R . The new correlation coefficient R can not only describe the case of a simple linear relationship, but also describe the case of a simple nonlinear relationship and the case of both simple linear relationship and nonlinear relationship. That is to say, the new correlation coefficient R can describe the internal law of any experimental data.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it