مقایسهٔ روش‌ها

	ضریب تورم واریانس (VIF)	شاخص شرط	رگرسیون حداقل مربعات معمولی (OLS)	رگرسیون ریج (Ridge Regression)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی	یادگیری ماشین
خانواده	Regression model	Regression model	Regression model	Machine learning
سال پیدایش	1970	1980	2019	1970
پدیدآور	Donald Marquardt	Belsley, Kuh & Welsch	Wooldridge (textbook treatment); classical least squares	Hoerl, A.E. & Kennard, R.W.
نوع	Diagnostic statistic	Collinearity diagnostic index	Linear regression	L2-regularized linear regression
منبع بنیادین	Marquardt, D. W. (1970). Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics, 12(3), 591–612.	Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. John Wiley & Sons. ISBN: 978-0-471-05856-4	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Hoerl, A.E. & Kennard, R.W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12(1), 55–67.
نام‌های دیگر	VIF, Variance Inflation Index, Multicollinearity Inflation Factor, Varyans Enflasyon Faktörü	Belsley Condition Index, Collinearity Condition Index, Singular Value Condition Index, Koşul İndeksi	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
مرتبط	3	2	5	4
خلاصه	The Variance Inflation Factor (VIF) is a scalar diagnostic statistic proposed by Donald Marquardt (1970) that quantifies how much the variance of an estimated regression coefficient increases due to linear dependence—multicollinearity—among the predictors in an ordinary least squares model. It is routinely applied in econometrics, social science, and biomedical research whenever analysts suspect that two or more independent variables move together closely enough to destabilize coefficient estimates.	The Condition Index, introduced by Belsley, Kuh, and Welsch (1980), is a scalar measure derived from singular value decomposition of the scaled regressor matrix. It quantifies the degree of near-linear dependence among predictors in ordinary least squares regression, enabling analysts to detect collinearity that inflates coefficient variance and destabilises parameter estimates. Widely used in economics, social sciences, and biomedical research wherever OLS regression is applied.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	Ridge Regression is an L2-regularized linear regression method, introduced by Arthur Hoerl and Robert Kennard in 1970, that reduces multicollinearity by adding a penalty on the size of the coefficients. It shrinks coefficients toward zero without setting any of them exactly to zero, producing more stable estimates when predictors are highly correlated.