a=[1 0;1 1;1 2]

a =

     1     0
     1     1
     1     2

b=[1;3;3]

b =

     1
     3
     3

ata=a'*a

ata =

     3     3
     3     5

atb=a'*b

atb =

     7
     9

c=ata\atb

c =

    1.3333
    1.0000

rmse=norm(a*c-b,2)/sqrt(3)

rmse =

    0.4714

a*c-b

ans =

    0.3333
   -0.6667
    0.3333

diary off