I am taking a theoretical approach to my multiple regression but the R squared and Adjusted R squared are both really low. I assume this means I can't improve my values with existing data and that the model is invalid? Can I do anything about it?

I am trying to test the causes of the intensity of organised violence (DV) in Somali, Ethiopia between 1997-2007 against a set of independent variables of: vegetation cover; population increase; population density; presence of export ban; livelihood type; and land degradation. My unit of analysis is a spatial region. I have 200 observations. All but the vegetation cover are dichotomous dummy variables. I have created the dataset using satellite imagery, census data, and maps.

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    $\begingroup$ At least you should precise how many observations and how many covariates you have. And is it a real dataset ? Do you have some reason to expect that the response is well associated to the covariates ? $\endgroup$ – Stéphane Laurent Mar 12 '12 at 20:34
  • $\begingroup$ R squared is a questionable thing to be using for much, see here: stats.stackexchange.com/questions/13314/… If you can outline what you are trying to do a bit more and tell us about the data I am certain someone will be able to give you a hand, but as it stands I can't tell you a ton. $\endgroup$ – asjohnson Mar 12 '12 at 20:34
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    $\begingroup$ For inspiration, and to illustrate what can be done even with existing data, create a dataset of the form $(x,y) = (\cos(t), \sin(t))$ for values of $t$ uniformly sampled in $[0, 2\pi)$. Regressing $y$ against $x$ should give near-zero adjusted $R^2$ values, but regressing $y^2$ against $x^2$ will give an adjusted $R^2$ of $1$. (The last two figures in stats.stackexchange.com/a/24265 show what's going on.) $\endgroup$ – whuber Mar 12 '12 at 21:25
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    $\begingroup$ It also depends on what type of data you have (e.g. social science data is notorious for giving low values compared to) and you haven't told us what you mean by "really low". You could simply be dealing with a relationship that has multiple causes, each of which have small effects. $\endgroup$ – Michelle Mar 13 '12 at 7:23
  • $\begingroup$ It sounds like you have panel or longitudinal data. Are your 200 observations actually 10 observations (one per year) for 20 regions? Or are they 200 observations for each region? Or 200 regions, with just one observation (eg an "average") that covers the time period. I certainly wouldn't despair yet; a low R-squared doesn't mean the model is useless, but we need more info to help. Are any of the variables showing up as statistically significantly different from zero? And what is the purpose of your model (eg prediction, general theoretical testing, or history). $\endgroup$ – Peter Ellis Mar 14 '12 at 10:42

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