I realize this should be simple, but even after reading over the several
help pages several times, I still cannot decide between the myriad "apply"
functions to address it.  I simply want to apply a function to all the rows
(or columns) of the same index from two (or more) identically sized arrays
(or data frames).

For example:

> a=matrix(1:50,nrow=10)
> a2=floor(jitter(a,amount=50))
> a
      [,1] [,2] [,3] [,4] [,5]
 [1,]    1   11   21   31   41
 [2,]    2   12   22   32   42
 [3,]    3   13   23   33   43
 [4,]    4   14   24   34   44
 [5,]    5   15   25   35   45
 [6,]    6   16   26   36   46
 [7,]    7   17   27   37   47
 [8,]    8   18   28   38   48
 [9,]    9   19   29   39   49
[10,]   10   20   30   40   50
> a2
      [,1] [,2] [,3] [,4] [,5]
 [1,]   31   56  -29  -13   10
 [2,]   38   61   71   55    9
 [3,]  -29   38   47   12   38
 [4,]   12    2   43   39   93
 [5,]  -43   23  -23   62    1
 [6,]  -13   61   55   11    2
 [7,]  -42    1   38   12    8
 [8,]  -13   -6  -18   16   95
 [9,]  -19   -2   78   33    1
[10,]   20  -16  -11   19   17

if I try the following for example:
apply(a,1,function(x) lm(a~a2))

I get 10 identical repeats (except for the list indexer) of the following:

[[1]]

Call:
lm(formula = a ~ a2)

Coefficients:
             [,1]       [,2]       [,3]       [,4]       [,5]
(Intercept)   8.372135  18.372135  28.372135  38.372135  48.372135
a21          -0.006163  -0.006163  -0.006163  -0.006163  -0.006163
a22          -0.093390  -0.093390  -0.093390  -0.093390  -0.093390
a23           0.009315   0.009315   0.009315   0.009315   0.009315
a24          -0.015143  -0.015143  -0.015143  -0.015143  -0.015143
a25          -0.026761  -0.026761  -0.026761  -0.026761  -0.026761

...Which is clearly very wrong, in a number of ways.  If I try by columns:
apply(a,2,function(x) lm(a~a2))
...I get exactly the same result.

So, which is the appropriate apply-type function when two arrays (or
d.f.'s?) are involved like this? Or none of them and some other approach
(other than looping which I can do but which I assume is not optimal)?
Thanks for any help.
-- 
Jim Bouldin, PhD
Research Ecologist

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