Rank Regression for a Multiple Regression
  Y_i = mu + Sum(j=1,p) X_{ij} beta_j + error_i
Specialized to p=1, so   Y_i = beta*X_i + mu
See Sections 9.6-9.7 in text
 
Data: Amount of pre-packed engine lubricant and engine survival times:
(Source of data unknown.)
 
Lubricant  Survival          Lubricant Survival
   1.  29     23           11.   84    429
   2.  21     36           12.   37    489
   3.  30     67           13.   94    504
   4.  45    104           14.   56    925
   5.  48    147           15.   67    980
   6.  92    164           16.   79   1254
   7.  74    247           17.   70   2961
   8.  61    304           18.   93   5351
   9.  99    355           19.   76   9915
  10.  24    408           20.   72  11301
 
Let X=Lubricant and Y=Survival (in days)

Within-sample tie groups:  X: 0   Y: 0
NO TIES in Xs or Ys
 
Finding the minimum value of D(beta):
  nw=190 nodes ranging from  -5527  to  5187
  Slope for beta<-5527: -2791.5   for beta>5187: 2791.5
Finding the lowest point on the curve Y = D(beta):
  At minimum value, lslope=-31.5  rslope=32.5     Qsum=2791.5
  Minimum attained at  beta=6.82813   D(beta)=256469
  Intercept:  mu=197.914  (median of Y_i-beta X_i Walsh averages)
 
Regression line and errors:
  E1 is mean of absolute values of residuals
  E2 is root-mean-square of residuals
  Rank-Regression:  Y =  6.8281 X +  197.914   E1=1615.16   E2=3355.82
 
See TheilRegression.txt for the corresponding results
  for Theil`s and least-squares regressions.