Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Passing through or lying on the same straight line.
 adj. Containing a common line; coaxial.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. lying on the same straight line
 adj. coaxial
from The Century Dictionary and Cyclopedia
 Lying in the same straight line.
 n. A tradename of a variety of anastigmat (which see).
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. lying on the same line
Etymologies
Sorry, no etymologies found.
Examples

One is the data set might be too small  what econometricians call "collinear"  and the other is that the assumptions that you need are not really credible.

No, not Newt's law, but Newton's Law, which says "The mutual forces of action and reaction between two bodies are equal, opposite and collinear."

However, I do though question your assumption that CO2 and Solar are collinear.

In the new setting, the projective properties of figures can be defined unexceptionably. a oneone mapping f of projective space onto itself is a collineation if it sends any three collinear points A, B, and C, to three points (A), (B), and (C), which are collinear too.

In fact, according to a common definition of “geometric duality”, the case of three lines sharing an intersection point can be considered equivalent to the case of three points being collinear.
Life on Mars? The real lesson from Lowell  The Panda's Thumb

Clearly if the drivers are nearly collinear you have a problem.

In a way principle component analysis helps as it orthoginilizes your drivers and although Steve mentioned the PCA is equivalent to least mean squares via the singular value based pseudo inverse this does not address the fact about the sensitivity of least mean squares to noise that correlates with the common signal of two nearly collinear drivers e.g co2 and solar.

It occurred to me that we can add extra error terms to introduce error in the cost function if the regression proxies are not collinear.

Since the low frequency parts of the CO2 curve and solar curve are nearly collinear the estimation is particularly sensitive to low frequency noise.

“This dichroic mirror layer blocks the diffusion by the address pits, allowing ideal collinear holographic recording,” it says.
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