Is there a concept called "contribution" in statistics? I am reading a research report. In that report, they used some elementary statistical methods to analyze their data. There is one quantity they computed called the contribution (of a factor), but they have not provided the definition for that. I am confused. I never heard of the contribution of a factor. It seems that they use these factors to build a linear model, e.g. $y=ax+b$. Does anyone know the meaning in this context? 
 A: It has no rigorous meaning. If I had to guess the context in which it was used, it may refer to the incremental reduction in sum of squared error attributed to adjusting for that factor, relative to a nested model which does not adjust for that factor. If that's the case, it may be demonstrating some seriously shortcomings in the understanding of statistics, since the goal (neither in prediction or inference) is not to make the sum of squared error vanish to zero (so "contribution" in this context means very little).
A: I'm not aware of a formal definition, but I've been using the term "contribution" with a different meaning from AdamO's in this paper:
C. Beleites, K. Geiger, M. Kirsch, S. B. Sobottka, G. Schackert and R. Salzer,
Anal. Bioanal. Chem., 400 (2011), 2801 - 2816., you can get the authors' manuscript here.
This is what I use it for and why:
Problem: I'm looking at spectroscopic data, i.e some kind of intensity at different wavelengths: each variate covers a different wavelength. As a spectroscopist, I can interprete  the physical/chemical/biological meaning of the different wavelengths.
For such data, each variate will span a different range, and it usually doesn't make sense to scale variates to common range or variance (you'd blow up the noise in variates with low signal, and I also need these differences for my interpretation).
When interpreting the meaning of linear models, I can look at the coefficients. However, coefficients alone are not the whole truth, I need to take into account the range of intensities for the respective variate.
If I say the linear model produces some kind of scores $\mathbf s$ by matrix-multiplying  $n$ spectra of $p$ wavelengths $\mathbf X$ with coefficients $\mathbf b$:
$ \mathbf s^{(n \times 1)} =  \mathbf X^{(n \times p)} \mathbf B^{(p \times 1)}$
with
$ s_{i} = \sum_{j = 1}^p x_{i, j} \cdot b_{j}$
Now,  I can put the the $x_{i, j} \cdot b_{j}$ into a matrix of the same size as $\mathbf X$. The columns correspond to the wavelengths. And each entry tells me how much of the final score of that spectrum is picked up at which wavelength, or which spectral band contributes how much and in which direction to the final score.
This allows me to do a spectroscopic interpretation of the model. These contributions are not real spectra, but they behave mostly like difference spectra with some additional possibilities. But I can relate them e.g. to known differences in the composition of my specimen.
For details, please look into the paper.

Edit: If this already has a name, or you could suggest a better one, I'd be happy to hear it.
