Srinivas in talking about the ADJUSTED R2.

I believe you have a small R2 which turns negative when you calculate the ADJUSTED R2.

As the adjusted R2 is given by {[(n -1)/(n-k)]*R2 + (1-k)/(n-k)}, you'll get a negative value whenever n

Hi, did you include a constant term in your regression? And what about estimated coefficients? Are they statistically significant?

Srinivas in talking about the ADJUSTED R2.

I believe you have a small R2 which turns negative when you calculate the ADJUSTED R2.

As the adjusted R2 is given by {[(n -1)/(n-k)]*R2 + (1-k)/(n-k)}, you'll get a negative value whenever n

Nino is correct about your R^2.

N=15 is probably too little data to get meaningful and significant results in any case.

To all,

Thank you very much for valuable suggestions

Hi,

a negative r2 usually indicates a wrong model assumption or your explanatory variables are not predictors to your explained variable. And increasing your data (n) will increase the value of your r2 (meaning give + value) but this does not mean your model is now correct. You need to conduct a correlation analysis first with your variables ( X's vs Y), then select only X's that has significant correlation with your Y. Also, make sure that your X's is not or does not have high (significant correlation) relation within the group of X's. If it does, you will have a problem of multicollinearity which will affect also your errors.

Your r2 simply measures the ability of your X's in explaining the variability or movement of your Y, a smaller r2 does not mean you did not get a good model, its just 1-r2 is the % of variability that your X's in your model did not measure.

Hope this helps a little in your problem.

By the way, with regards to putting a constant term in your model, my take on that is, it depends on your expectation of your Y variable. In a purely statistical or mathematical point of view, you will really obtain a constant term, either 0 or any value > 0. However, in economics point of view, there are instances wherein a prediction model does not have a constant term (Beta 0) or does not have a y intercept, you can google some examples of these models.

Nino above has answered your question. I just wanted to clarify something what the first two commenters wrote. When you omit the constant term, you basically don't use R2. Use it as a standard rule.

What software that you make OLS regression? The problem may be caused by the software, it make mistake in calcaulating TSS or RSS. Make the regression using other econometric softwares.

I am getting negative Adjusted R2, when I am running a barro-regression to test absolute or conditional convergence hypothesis. Here, the dependent variable is current value of State Per capita Domestic Product and Predictor variable is initial State Per Capita Domestic Product. I run same regression in STATA-10.1 software for Literacy rate, TFR, IMR, LEB other demographic indicators, but I am seeing a negative value specifically for Economic Indicator that is State Per capita Domestic Product. The sample size and procedure and software are same for all the indicators considered for convergence analyses.

Are you working with cross-sectional data? How many countries and how many years are you working with?

Yes, i am working on cross-sectional data. Sample size 15, includes 15 major states of India. Though, India comprises 28 states (provinces), but we do not have long-term data for all the 28 states. I am using 31 years of State Per Capita Domestic Product data across the 15 states.

i heard this case from my lecture. she said, it might be because there is something with your data. maybe you can try to transform it. maybe into antilog form or log something like that. but i think maybe you should try with more samples. because as far as i know R2 shouldn't be negative. if you get it negative, there is something wrong with your data or analysis.

Do I understand it correctly that you are using 15 states for a period of 31 years, or not? If so, you are actually using panel data. 15 states might still be a low number of different observations to distinguish between within and between coefficients.

Some idea to improve results:

Check for the correlation between your dependent and independent variables, because they might be rather low in the case of a low adjusted R-squared.

Try a model with only one explanatory variable with a coefficient per state and check whether the coefficients are similar or significantly different. In the latter case, the coefficients are state-specific and you have to take it into account when doing your regressions to improve your results.

QUESTION: I am having a negative adjusted R^2 (i.e. -0.14) while my number of observations is 50 and I have 10 predictors in the model. The R^2 is found to be 0.170.

While I am using the formula above (from Nino) and I don't get this result, I am wondering whether there are any other factors that could affect the result being negative...

Where does the "-0.14" came from? Is it the output of the software? And what type of regression model are you running? Confirm to me the number of observations and predictors.

The conclusion will terrorise the entire academia.