[R] Fit a 3-Dimensional Line to Data Points

[Hans W. Borchers]

S. M. Niaz Arifin <niazarifin <at> yahoo.com> writes:
> 
> Hi Experts,
> I am new to R, and was wondering how to do 3D linear
> regression in R. In other words, I need to Fit a
> 3-Dimensional Line to Data Points (input).
> 
> I googled before posting this, and found that it is
> possible in Matlab and other commercial packages. For
> example, see the Matlab link:
>
http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/orthoregdemo.html#10
> 
> Is there a way to achieve this in R?

As a short self-test I translated the Matlab code into R where we take
as "best fit" the first principal component -- as in the Matlab example.

# I copied the Matlab matrix see below; load it from there first.
# X <- matrix(scan(stdin()), ncol=3, byrow=TRUE)
#   -0.4326   -1.0767   -0.9895
#   ...
#

  N <- nrow(X)

  meanX <- apply(X, 2, mean)
  Xpca   <- princomp(X)
  dirVector <- Xpca$loadings[, 1]

  Xfit1 <- matrix(rep(meanX, each=N), ncol=3) + 
             Xpca$score[, 1] %*% t(dirVector)
  t <- c(min(Xpca$score[, 1])-.2, max(Xpca$score[, 1])+.2)
  endpts <- rbind(meanX + t[1]*dirVector, meanX + t[2]*dirVector)

  library(scatterplot3d)
  s3d <- scatterplot3d(X[, 1], X[, 2], X[, 3], color="blue")
  s3d$points3d(endpts[, 1], endpts[, 2], endpts[, 3], type="l",
               col="red", lwd=2)

I leave it as an exercise to add the straight perpendicular segment from
the points to the line.

You can look at it interactively applying the RGL package !

Hans Werner Borchers


P.S.:   Definition of X copied from the Matlab example

X <- matrix(scan(stdin()), ncol=3, byrow=TRUE)
   -0.4326   -1.0767   -0.9895
   -1.6656    0.2689   -2.7947
    0.1253    0.5225    0.7053
    0.2877    1.7158   -0.4033
   -1.1465    0.3500   -0.6580
    1.1909   -0.3924    1.0894
    1.1892    0.6105    0.7931
   -0.0376   -0.9963   -0.5846
    0.3273    0.0463   -0.4308
    0.1746   -0.0123   -0.1329
   -0.1867   -0.0373   -0.9605
    0.7258   -0.1663   -0.1853
   -0.5883    0.9552    0.4620
    2.1832   -1.3995    1.8350
   -0.1364    0.3923   -1.0084
    0.1139    0.9003   -0.0771
    1.0668    0.9295   -0.1472
    0.0593    0.5780   -0.9852
   -0.0956    0.0204   -0.2554
   -0.8323    0.4969   -0.0122
    0.2944    0.6163    0.2148
   -1.3362   -0.5177   -0.4395
    0.7143   -0.2270   -0.2632
    1.6236    0.0348    0.8565
   -0.6918   -1.5837   -0.4571
    0.8580   -0.0577   -0.2148
    1.2540    0.3669   -0.0623
   -1.5937   -0.0103   -0.5090
   -1.4410    1.1262   -1.2071
    0.5711   -0.2297   -0.0015
   -0.3999    0.5307    0.1948
    0.6900    0.9209    0.5309
    0.8156    1.0850   -0.2560
    0.7119   -0.8297    1.5774
    1.2902    0.4658    1.0754
    0.6686    0.3668    1.4688
    1.1908   -0.7492    1.7739
   -1.2025   -0.9675   -1.2144
   -0.0198    1.0565   -1.0725
   -0.1567   -0.1602   -0.1419
   -1.6041    0.0612   -1.4099
    0.2573    0.1377   -0.4227
   -1.0565   -0.8339   -0.3004
    1.4151   -0.2652    2.1121
   -0.8051    0.2737   -1.0093
    0.5287   -0.8250   -0.0866
    0.2193    0.8093   -0.1305
   -0.9219    0.3731   -0.2627
   -2.1707   -1.2392   -1.9997
   -0.0592   -0.2721   -0.8440

#EOF