how to generate a linear regression matrix like cor()

Question

I have a dataframe like below :

  a1 a2 a3 a4
1  3  3  5  5
2  4  3  5  5
3  5  4  6  5
4  6  5  7  3

I want to do linear regression for every two columns in the dataframe, and set intercept as 0.

In other words, I want to get the coefficients of lm(a1~a2+0), lm(a1~a3+0), lm(a1~a4+0), lm(a2~a1+0), lm(a2~a3+0)...

In cor(), if I input a dataframe, I will get a matrix back, e.g. below,

          a1        a2        a3        a4
a1 1.0000000 0.9467293 0.8944272 0.2045983
a2 0.9467293 1.0000000 0.9622504 0.4989222
a3 0.8944272 0.9622504 1.0000000 0.4574957
a4 0.2045983 0.4989222 0.4574957 1.0000000

In lm() is there any way to get the same kind of matrix?

Thanks.

Answer 1

Here's a pretty general strategy

dd<-read.table(text="a1 a2 a3 a4
1  3  3  5  5
2  4  3  5  5
3  5  4  6  5
4  6  5  7  3", header=T)

mm<-diag(ncol(dd))
mm[lower.tri(mm)] <- combn(dd, 2, function(x) coef(lm(x[,2]~x[,1]+0)))
mm[upper.tri(mm)] <- rev(combn(dd[length(dd):1], 2, function(x) coef(lm(x[,2]~x[,1]+0))))

This gives the matrix

mm
#           [,1]     [,2]      [,3]      [,4]
# [1,] 1.0000000 1.202381 0.7738095 0.9285714
# [2,] 0.8255814 1.000000 0.6592593 0.7925926
# [3,] 1.2441860 1.508475 1.0000000 1.2033898
# [4,] 0.9069767 1.101695 0.7481481 1.0000000

where element [4,1] is the same as coef(lm(a4~a1+0, dd)) and element [2,3] is the same as coef(lm(a2~a3+0, dd))