Some of these are discussed below. It is important to know what these methods are. Estimates based on a bounded phi reduce the influence of large deviations in y. Estimates based on a phi which asymptotes to 0 in both directions do even better. Often we need to smooth or interpolate data. Polynomial regression can be used to fit a smooth curve to data.
Trend lines are the simplest examples.
Orthogonal polynomials are easier to work with and interpret. Fit polynomial patches to the data so that the patches are smoothly connected. Generalized additive models. Another way to estimate the relation. The more flexible the fitted model, the more variable the predictions.