Exploring the Effects of Assumption Violations on Simple Linear Regression and Correlation Using Excel
Bibliographic record
Abstract
Regression analysis plays a central role in statistics and our understanding of the world. Linear regression models are the simplest type of regression and an understanding of them is an essential basis for more advanced models. In this article we will show how to use Excel to generate data from a simple linear regression model and illustrate how the statistical methods behave both when the fundamental assumptions of the model hold and when the fundamental assumptions are violated. The advantage of the using the program Excel is that when you press the recalculate button, under the Formulas menu, the data that is generated at random will be regenerated, statistical calculations will be recalculated and relevant graphs will be redrawn. Least squares is the statistical technique typically used when assumptions are satisfied. A statistical technique used when the normality assumption is violated is the non-parametric technique introduced by Kendall and Theil. The latter is useful when data are skewed or heteroskedastic, and is as powerful as least squares regression for Normally distributed data. Exercises are provided to illustrate both these procedures. In these exercises we generate samples of a Simple Linear Regression where the error term could follow a Normal distribution or the heavy tailed t-distribution.
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How this classification was reachedexpand
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 | 0.000 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".