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Imperfect multicollinearity refers to a situation where the predictive variables have a nearly exact linear relationship. Contrary to popular belief, neither the Gauss–Markov theorem nor the more common maximum likelihood justification for ordinary least squares relies on any kind of correlation structure between dependent predictors [ 1 ...
Perfect multicollinearity refers to a situation in which k (k ≥ 2) explanatory variables in a multiple regression model are perfectly linearly related, according to
Analyze the magnitude of multicollinearity by considering the size of the (^). A rule of thumb is that if (^) > then multicollinearity is high [5] (a cutoff of 5 is also commonly used [6]). However, there is no value of VIF greater than 1 in which the variance of the slopes of predictors isn't inflated.
In the more general multiple regression model, there are independent variables: = + + + +, where is the -th observation on the -th independent variable.If the first independent variable takes the value 1 for all , =, then is called the regression intercept.
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 is the problem of multicollinearity in moderated regression. Multicollinearity tends to cause coefficients to be estimated with higher standard errors and hence greater uncertainty. Mean-centering (subtracting raw scores from the mean) may reduce multicollinearity, resulting in more interpretable regression coefficients.
Heteroscedasticity often occurs when there is a large difference among the sizes of the observations. A classic example of heteroscedasticity is that of income versus expenditure on meals. A wealthy person may eat inexpe
In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag.