regression

Regression is a specific kind of statistical method for modeling relationships between variables. A competent speaker would call regression 'a type of statistics/statistical method.' Files against the nearest kind: statistics.

Regression analysis is a statistical method built and maintained for the sake of statistical inference — specifically for inferring relationships between variables and making predictions. Its primary purpose in practice is to serve statistical inference about data-generating processes. Law 8d: servant points at master.

A logistic regression is a specific kind of regression used to model the probability of a categorical dependent variable. It extends linear regression with a logistic link function. A competent speaker in statistics would call logistic regression 'a regression'. Direction: logistic regression INSTANCE_OF regression (specific→general, Law 9).

TESTED: residual analysis depends on regression — remove regression/prediction models and residual analysis stops OPERATING. Residuals (observed minus predicted values) only exist within a regression framework; without regression models as the reference, there are no residuals to analyze. Present-tense operational dependency, not historical association.

A smoothing spline IS a specific kind of regression method that fits a smooth curve through data points using piecewise polynomials with continuity constraints at knots. It answers the question of regression — estimating a function from data — using spline basis functions. A competent speaker would call it 'a regression' method.

Influence plot IS built and maintained for the sake of regression analysis. Its designed purpose is to identify influential data points in regression models, quantifying how each observation affects coefficient estimates. The test: for whose sake? The plot serves regression — the servant (influence plot) points at the master (regression).

dfits measures the influence of each observation on fitted regression values. It is built and maintained as a diagnostic tool specifically for regression analysis — its designed purpose is to serve regression by quantifying which data points disproportionately affect model fit.

Cook's distance is a regression diagnostic designed specifically to measure observation influence on the overall fitted model. Its purpose is to serve regression analysis by identifying influential data points that disproportionately affect model parameters.

dfbeta measures the change in each regression coefficient when an observation is deleted. Its designed purpose is to serve regression analysis by identifying observations that disproportionately influence parameter estimates. For whose sake? regression.

Cook's distance measures how much the regression fit changes when an observation is deleted. Its designed purpose is to serve regression analysis by identifying influential data points.

influence diagnostics is built for the sake of regression analysis — its designed purpose is to identify influential observations that distort regression estimates and predictions, directly serving the integrity of regression.

Regression as a statistical method predates the formal concept of multicollinearity; the phenomenon was identified within regression analysis and the term was coined to describe it. Which came first test: regression (18th-19th century) clearly predates the concept of multicollinearity (20th century).

Standardized residuals require a regression model to operate — they are residuals scaled by the model's error structure. Remove regression and standardized residuals have no mathematical framework to function.

Partial regression plots visualize the contribution of individual predictors within a regression model. Remove regression and the plot has no framework to operate — it cannot be computed, interpreted, or displayed.

A component-plus-residual plot (also called a partial residual plot) is a regression diagnostic tool that derives from regression analysis. Regression as a statistical method existed first and fed into the development of diagnostic visualization techniques. The plot shows the relationship between a predictor and the response AFTER accounting for other predictors in the regression model — it is a derivative visualization built on the regression framework.

Influential observations are defined by their effect on regression models (Cook's distance, DFBETAS measure impact on regression coefficients). Remove regression and the concept of influential observation ceases to operate.

Omitted variable bias arose from regression analysis — when relevant variables are excluded from a regression model, coefficient estimates become biased. The concept emerged from the practice of regression modeling.

The durbin watson test detects autocorrelation in regression residuals. Its operational meaning is tied to regression — remove regression and the test has nothing to operate on. Passes the removal test of Law 8.

The breusch-pagan test detects heteroscedasticity in regression residuals. Its entire operational framework is regression — remove regression and the test has no residuals to analyze. This passes the Law 8 removal test.

Diagnostic plots are built for the sake of regression — they are designed to check regression assumptions, detect outliers, and evaluate model fit. Servant→master direction correct.

Linear prediction is a specific kind of regression applied to temporal data — it estimates future values from past observations via linear combinations. A competent speaker would call linear prediction a form of regression.

Probit model is a specific kind of regression model for binary outcomes — a generalized linear model with probit link function. A competent speaker calls a probit model 'a type of regression.' Nearest kind: regression (not a leap — regression is the direct parent category for model families like linear, logistic, and probit).

DFFITS computes the influence of deleting a data point on regression-fitted values. It requires a fitted regression model as its operational basis — residuals, hat values, and coefficient estimates. Remove regression and dffit has no model to operate on.