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An international trend lines
One that the simplest approaches to identify trends is to fit a ordinary least squares regression design to the data. The version most world are familiar with is the direct model, yet you can include other polynomial terms for extra flexibility. In practice, protect against polynomials of levels larger than three since they are less stable.
ll.smooth = loess(xx~tt, span=0.75)ll.pred = predict(ll.smooth, se = TRUE)ll.df = data.frame(x=ll.smooth$x, fit=ll.pred$fit,lb = ll.pred$fit - (1.96 * ll.pred$se),ub = ll.pred$fit + (1.96 * ll.pred$se))ll.df = ll.df