Method - Lowess
main topic 

The lowess routine calculates a new, smoothed y-value for each x-value.

1    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. The selection often results in more points selected from one side of the x-value than the other. The example below 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.

Y-Values

 

X-Values

2    Minitab calculates weights using the x-distance between each point in the selected fraction and the point to be smoothed:

weight = [1 - (

distance from the selected point

max distance between selected point and the (f·n) points

)3]3

This equation produces weights for the fraction of selected points that have the following relationship:

 

X-range for the fraction

Weights

 

X-Values

Points closest to each x-value have the greatest weight in the smoothing.

3    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.

4    Finally, the Minitab limits the influence of outliers on the results by using further iterations (default n = 2) of step 3 (called "robust steps"), with new weights calculated as follows:

weight = [1 - (

|residual for the point from previous step|

6 (median of all |residuals| from previous step)

)2]2