df.p <- plm.data(df, c("uid", "year")

reg1 <- plm(pens ~ woman + age + I(age^2/100) + high + medium + nord + centre, model="within", effect="twoways", data=df.p)

summary(reg1)

Error in crossprod(t(X), beta) : non-conformable arguments

p1 <- with(df, data.frame(woman=woman, age=age, high=high, medium=medium, nord=nord, centre=centre))

round(cor(p1),3)

vif(p1)

No variable from the 20 input variables has collinearity problem.