On 26 Jun 2003, Will wrote: > Back to DW's question - I don't know of any NP Regression tool, so, > Donald, if you do please enlighten me.
The following is due to John Tukey and may be found in Tukey, "Exploratory Data Analysis" (Addison-Wesley, 1977 I think) or, more likely, in Mosteller & Tukey, "Data Analysis & Regression" (Addison- Wesley, same year or the next). Start with a scatterplot of Y vs X. Divide the plot into nine vertical bars of approximately equal width (that is, divide the range of X into nine segments). In each bar, find and plot the joint median. Connect the joint medians in the three leftmost bars: if the Y:X relationship is approximately linear, this will produce a very flat, sloping triangle. Do the same with the three center bars; and with the three right-most bars. Find (approximately) the center of gravity of each triangle. Use the leftmost and rightmost c.g.s to define the slope of the line, and the center c.g. to adjust the line vertically so as to minimize the departures of the three c.g.s from the line. All of this is originally described in terms suitable for analysis by hand and by eye, and assumes the scatterplot is not so dense as to present difficulties in determining where the nine joint medians are. Presumably a clever programmer could automate the procedure. The question of how to test hypotheses about values of the slope is not so simply dealt with, however, and I have little advice to offer on that point. (Of course, one needs to remain observant: part of the reason for using 9 slabs, and then finding 3 c.g.s, is to be able to see (if it should be the case) that the relationship in question is NOT linear, so that a straight-line slope estimate would not be very helpful.) Extending the method to cases with two or more predictors rather than only one would presumably be possible, but presents some additional challenges, and I am not sure it would be worth the effort. Notice that the method presupposes that the variables X and Y are in themselves meaningful; so the method is not in fact "non-parametric" in the sense that rank-order methods are held to be non-parametric. -- DFB. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
