Regression Diagnostics Guard

OLS regression produces estimates that are optimal (BLUE) only when its assumptions are met: linearity, homoscedasticity of residuals, normality of residuals, and absence of influential outliers. When these assumptions fail, the estimates are biased and the standard errors are wrong. The diagnostics that detect these failures take seconds to run and are almost never reported in published papers.

STEP 1 —The Pitfall

The practical consequence of undiagnosed assumption violations: heteroscedastic residuals inflate standard errors for some coefficients and deflate them for others, making some estimates appear more significant than they are while making others appear less significant. A single highly influential point (high Cook's distance) can reverse the sign of a regression coefficient while changing the Rﾂｲ by less than 5% —invisible without diagnostics.

Multicollinearity (high VIF) does not bias the point estimates but dramatically inflates standard errors, making individually significant predictors appear non-significant when included together. It also makes coefficient estimates highly unstable and uninterpretable.

[Image placeholder: 4-panel diagnostic plot: (1) Residuals vs. Fitted —shows heteroscedasticity pattern (funnel shape), (2) Normal Q-Q —shows heavy tails, (3) Cook's Distance —shows one point with D > 1 (critical threshold), (4) VIF bar chart —shows two predictors with VIF > 5. Each panel labeled with the assumption it tests and the consequence of violation.]

Standard 4-panel OLS diagnostics: each panel detects a specific assumption violation. All four should be checked before reporting regression results.

STEP 2 —Journal Requirement

Most biostatistics and epidemiology journals require that regression assumption checks be reported. Methods sections should state: "Regression assumptions were checked using residual diagnostic plots. [Violations / No violations were detected]." If violations are detected, the response —transformation, robust regression, alternative model —must be stated.

STEP 3 —Licklider Solution

Input

Fitted OLS regression model
Predictor variables and their scales

Output

Residuals vs. Fitted: tests linearity and homoscedasticity. Breusch-Pagan test for formal heteroscedasticity detection.
Normal Q-Q of residuals: Shapiro-Wilk test on residuals (n 竕､ 50) or Anderson-Darling (n > 50)
Cook's Distance: data points with D > 4/n flagged as potentially influential. Points with D > 1 flagged as highly influential.
VIF: predictors with VIF > 5 flagged as moderate multicollinearity; VIF > 10 flagged as high multicollinearity
Diagnostic summary badge: Pass / Warning / Fail per check
Response recommendations: log transformation, robust regression (Huber M-estimator), predictor removal or combination for multicollinearity

Guard

For confirmatory regression analyses, the diagnostic check must be completed before export. A Fail on any diagnostic dimension (severe heteroscedasticity, non-normal residuals with n < 50, Cook's D > 1, VIF > 10) requires either: correction and re-analysis, or explicit disclosure that the violation was detected and its potential impact on the reported estimates.

[Image placeholder: Licklider regression diagnostics panel showing: 4-panel diagnostic grid with automated test results overlaid (Breusch-Pagan p-value, Shapiro-Wilk on residuals, max Cook's D, max VIF), and a summary diagnostic badge showing Pass / Warning / Fail for each dimension.]

Regression diagnostics panel: 4-panel grid with automated test results and per-dimension Pass/Warning/Fail badges.

STEP 4 —Draft Output (Draft / Needs review)

OLS regression assumptions were assessed using standard diagnostic procedures.
Residual vs. fitted plots and Breusch-Pagan test indicated homoscedasticity
(BP = 2.1, p = 0.35). Residuals were approximately normally distributed
(Shapiro-Wilk: W = 0.97, p = 0.43). No influential observations were
identified (maximum Cook's D = 0.18, threshold 4/n = 0.10; this point
was retained as it met all inclusion criteria). Variance inflation factors
were all < 3.0, indicating absence of multicollinearity.