I have used best subset regression with various selection criteria (e.g. Mallow's Cp and AIC) to compile a list of possible regression models to explain the response variable "Length". Below is the best model of the bunch,
Length = 5.770 + 0.1180 Max flow field width + 0.02691 time until ff + 0.1897 Duration of FF - 0.0465 Cooling dominate phase
however the coefficient for "cooling dominate phase" is negative in the regression but it has a positive correlation to the response variable. Here is the table correlation coefficients for the response and predictor variables in the model.
The VIF scores are all under 2 but being above 1 it suggests there is some degree of collinearity or multicollinearity happening. Here are the VIF's.
Can I still have confidence in the accuracy of the regression coefficients if the VIF's are low but the sign of a predictor variable coefficient is opposite from its correlation to the response variable?