Final answer:
The smallest possible value of VIF is one, which indicates the absence of multicollinearity and that predictor variables in a regression model are not correlated.
Step-by-step explanation:
The smallest possible value of the Variance Inflation Factor (VIF) is one. The VIF is used to measure how much the variance of an estimated regression coefficient increases due to multicollinearity. Multicollinearity occurs when predictor variables in a regression model are correlated. When there is an absence of multicollinearity, the predictor variables are not correlated, which implies that each predictor has a unique contribution to the prediction model without redundancy.
VIF values provide an indication of the presence of multicollinearity. A VIF of 1 suggests no correlation between the predictor variable and any other predictor variables, and hence, no multicollinearity. When the VIF exceeds values of 5 or 10, it indicates a potentially problematic level of multicollinearity, and the estimation of coefficients may be unreliable.
The correlation coefficient, denoted as r, is another related statistic that measures the strength and direction of a linear relationship between two variables. A value of r equal to 1 or -1 signifies a perfect linear relationship, while a value of 0 indicates no linear relationship. In the context of VIF, when all pairwise correlation coefficients between predictors are zero, each VIF for the predictors in the model would be one.