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# Linear Regression with Independent Variable with many zeros

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• 13-05-2021 1:39am
Registered Users Posts: 4

When I have a dataset where one of my independent variables is all zeroes, this is obviously a rank deficient matrix and they regression cannot be performed. When I have a dataset that has an indicator/dummy variable that many zeros (let's say 95 out of 100) is this ok ? Here's a matlab example illustrating.
```A = rand(100,100);
inverseATA = inv(A' * A);
all(all(isfinite(inverseATA)))

B = rand(100,100);
B(1:90,2) = 0;
inverseBTB = inv(B' * B);
all(all(isfinite(inverseBTB)))

C = A;
C(1:99,2) = 0;
inverseCTC = inv(C' * C);
all(all(isfinite(inverseCTC)))

D = rand(100,100);
D(:,1)  = 0;
inverseDTD = inv (D' * D);
all(all(isfinite(inverseDTD)))
```

It appears that there is no issue here, but I can't find anything in any of my text books or online backing this up either, outside of a one liner here and there saying it's fine. I'd like a bit more detail on it.

Thanks.

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#2
Moderators, Science, Health & Environment Moderators Posts: 1,847 Mod ✭✭✭✭

Hello Billynose. It really depends on what you're trying to do. Can you give us more info? Why are you trying to fit a line to data?

It's not clear (to me) what is going on with your MATLAB code, or what your end objective is. Can you provide a minimal example with comments?

• Options
#3
Registered Users Posts: 4

What I'm trying to do is to seeif my set of independent variables are still viable (I guess you could say well conditioned) to perform a regression on. The matlab code is basically checking that (X'X)^-1 is not singular. I run through 4 examples.
with a 100 x n matrix

A is the base case
B takes one column and converts 95 of the values to 0
C takes one column and converts 99 of the values to 0
D takes one column and converts all of the values to 0

D is obviously rank deficient, but B and C are not. I've tried looking at the condition number as well, but I actually don't see much of a difference between A and B. There is an increase up to C though.