Smoother lines are most useful when the curvature of the relationship does not change sharply. Smoother lines added to graphs are calculated using the lowess smoothing method.
In this time series plot, one smoother line is solid and the other smoother line is dashed.
You can add a lowess smoother line to scatterplots, matrix plots, histograms, and time series plots.
After a smoother line is added to a graph, you can change its color, size, type, and parameters.
The lowess smoothing method is a common technique for determining a smoothing line. Lowess stands for locally-weighted scatterplot smoother. You can specify parameters to modify both the degree of smoothing and the effect of outliers.
The lowess routine calculates a new, smoothed y-value for each x-value.
The routine selects a fraction (default f = 0.5) of all points, using the data closest in x-value on either side of the (x,y) point. This fraction is called the degree of smoothing. The selection often results in more points selected from one side of the x-value than the other. The following example shows the fraction of data selected for a given point. The shaded area holds the 0.5 fraction closest to the solid red data point.
Minitab calculates weights using the x-distance between each point in the selected fraction and the point to be smoothed:
The following graph shows the relationship between the weights (vertical axis) and the x-values (horizontal axis) for the fraction of selected points. Points closest to each x-value have the greatest weight in the smoothing.
Minitab performs a weighted linear regression on all points in the selected fraction of the data, using the weights from step 2 to produce an initial smoothed value.
Finally, Minitab limits the influence of outliers on the results by using further iterations (default n = 2) of step 3 with new weights calculated as follows: