Non-parametric regression methods

Another rank correlation coefficient, due to Kendall, was introduced in 1938. it claims to have some theoretical advantages over the Spearman method, but is harder to calculate (especially when tied ranks occur) and is not so frequently used. 

Theil s method determines the slope of a regression line as the median of the slopes calculated from selected pairs of points the intercept of the line is the median of the intercept values calculated from the slope and the coordinates of the individual points. 

The method assumes that a series of points (x, y, X2, etc. is fitted by a line of the form y = a + bx. The first step in the calculation involves ranking the points in order of increasing x. If the number of points, x, is odd, the middle point, i.e. the median value of x, is deleted the calculation always requires an even number of points. For any pair of points x, y, Xj, yy) where x, x the slope, b,j, of the line joining the points can be calculated from  

The following results were obtained in a calibration experiment for the absorp-tiometric determination of a metal chelate complex  

Use Theil s method to estimate the slope and the intercept of the best straight line through these points. 

---