Nonparametric methods have also been devised for regression. Here€™s a simple way to estimate the slope: For each pair of subjects, the slope of the line connecting their two points is the difference between their y values divided by the difference between their x values. (See the figure.) With n subjects, we can find this slope for each pair of points. (There are n (n - 1)/2 pairs of points.) A nonparametric estimate of the slope is the median of all these slopes for the various pairs of points. The ordinary slope (least squares, minimizing the sum of squared residuals) can be strongly affected by a regression outlier. Is this true also for the nonparametric estimate of the slope? Why or why not?

Statistics The Art and Science of Learning from Data

3rd edition

Authors: Alan Agresti, Christine A. Franklin

ISBN: 978-0321755940

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