Search results
Results from the WOW.Com Content Network
Excluding variables with a high variance inflation factor also invalidates the calculated standard errors and p-values, by turning the results of the regression into a post hoc analysis. [14] Because collinearity leads to large standard errors and p-values, which can make publishing articles more difficult, some researchers will try to suppress ...
In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). PCR is a form of reduced rank regression. [1] More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model.
Lack of perfect multicollinearity in the predictors. For standard least squares estimation methods, the design matrix X must have full column rank p; otherwise perfect multicollinearity exists in the predictor variables, meaning a linear relationship exists between two or more predictor variables. This can be caused by accidentally duplicating ...
The VIF provides an index that measures how much the variance (the square of the estimate's standard deviation) of an estimated regression coefficient is increased because of collinearity. Cuthbert Daniel claims to have invented the concept behind the variance inflation factor, but did not come up with the name. [2]
Multicollinearity is the phenomenon where the correlation between two explanatory variables is very high. A high level of correlation between two such variables can dramatically affect the outcome of a statistical analysis, where small variations in highly correlated data can flip the effect of a variable from a positive direction to a negative ...
To detect multi-collinearity among the predictors, one can conduct a linear regression analysis with the predictors of interest for the sole purpose of examining the tolerance statistic used to assess whether multi-collinearity is unacceptably high. Sparseness in the data refers to having a large proportion of empty cells (cells with zero counts).
Partial least squares (PLS) regression is a statistical method that bears some relation to principal components regression and is a reduced rank regression [1]; instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space of maximum ...
Standardized coefficients shown as a function of proportion of shrinkage. In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.