Can somebody explain to me the difference between linear model and loess model in statistics? I need to explain this to non-math people.
A VERY non-technical answer
A simple linear model fits a straight line through a set of points. The line is the best possible straight line (at least, for one sensible definition of best)
A loess model fits a complicated curve through a set of points. In some ways, it can be thought of as a complicated moving average. It is the best possible curve (at least, for one sensible definition of best)
loess.demo function in the TeachingDemos package for R will interactively demonstrate the ideas behind a loess fit. It will plot a set of data and the loess fit, then when you click on a point it will show the window used to fit at that point, the relative weights of the points within the window, and the "linear model" fit to that weighted data. Clicking on additional points will then update the display to show the general concept of the loess fit.
This may help explain what loess does and may help in an explanation of the difference.
Here is a simple but detailed response.
A linear model fits a relationship through all of the data points. This model can be first order (another meaning of "linear") or polynomial to account for curvature, or with splines to account for different regions having a different governing model.
A LOESS fit is a locally moving weighted regression based on the original data points. What's that mean?
A LOESS fit inputs the original X and Y values, plus a set of output X values for which to compute new Y values (usually the same X values are used for both, but often fewer X values are used for fitted X-Y pairs because of the increased computation required).
For each output X value, a portion of the input data is used to compute a fit. The portion of the data, generally 25% to 100% but typically 33% or 50%, is local, meaning it is that portion of the original data closest to each particular output X value. It is a moving fit, because each output X value requires a different subset of the original data, with different weights (see next paragraph).
This subset of input data points is used to perform a weighted regression, with points closest to the output X value given greater weight. This regression is usually first order; second order or higher is possible, but require greater computation power. The Y value of this weighted regression calculated at the output X is used as the model's Y value for this X value.
The regression is recomputed at each output X value to produce a full set of output Y values.