Make sure you have an intercept in the model.

If you do have an intercept, it's possible that the model just doesn't explain any variation in the dependent variable.

But I would also start by looking at the relationships between each independent variable or confounder and the dependent variable.

And look at residual plots. It's possible there's an outlying value with a lot of leverage or influence.

Thank you for your answer; it was helpful, I removed a few outliers and noticed the adjusted R-square increased from -0.006 to 0.0038.

0.0038 is too low, and overall, F is still non-significant.

I am not sure how to report this as all the independent and confounders are non-significant.

Before fitting the multiple regression model, I performed univariate analysis to see the effect of the independent variable and any of the confounders on the outcome; all of them were non-significant.

sometimes, clinicians expect us to do miracles to provide confidence to support their hypotheses.

Bahar

Oh, don't remove the outliers, that's a bit outright cheating.

As Sal said, what is the intercept?

What you can do it, instead of linear regression (though I don't know your data), you may fit another function (quadratic, exponential,...) though this would be something you would need to justify.

Thanks for your answer; I have included intercept in the model.

All the figures for the dependent variable are not positive to apply exponential or gamma regression.

I also wanted to fit exponential as the dependent variable, and residual is a little right-skewed, but I think I can't because of the range.

I also fitted univariate analysis for each confounder and independent variable and saw there was no significance at all.

In this case this may be just the actual outcome - you don't have any uni- or multi-variate correlation between the confounders and independent variables. But a result is a result as they say ;)

Thanks so much for your help

There may be a substantial problem (all B’s are approximately zero), the correlation matrix may be inconsistent, or there are too many predictors.

As R2 is zero or positive by definition, and Adj.R2 is

1-(1-R2)*(NCases-1)/(NCases-NPredictors-1), Adj.R2 may become negative with large NPredictors. For instance, if R2=10% and N=100, Adj.R2 is 1% with 9 predictors, but -0,1% with 10 predictors. If this is the case, remove irrelevant and/or insignificant predictors.

Inconsistent matrices may be the result of pairwise deletion, when the correlations are not calculated on exactly the same cases. In that case use listwise deletion and/or remove predictors with many missings.

Finally, if R2 was near zero to begin with, and so all B’s were near zero as well, you (and especially your client) has to accept that ‘nothing’ was found. But remember the old saying ‘Absence of proof is not proof of absence’. Null-results may be either because there are really none in the population, but also because the research had simply not enough power to detect those results, for instance because of too few cases (note that the ‘alpha’-error is something else than the ‘beta’-error).

Thanks for the great explanation; all the betas are near zero.

There is no missing value.

I have only one independent variable and three confounders; I have run with even one predictor. There would be too low Adjusted R square such as 0.005.

There is no multicollinearity as well.

Well, in econometrics, a negative adjusted R2 is a serious issue of concern that needs to be properly checked. In the first place it is a clear signal for spurious regression. A spurious regression is nothing but indicating the failure of the independent variable in explaining the dependent variable. It also indicates the porosity of the data used in the study. Most importantly, it indicates serious problems associated with the model of the study and that the study is baseless and has no significance, value, and direction.

However, the foregoing issues can be addressed and have a very good results/outcomes. The following steps could be of great help if taken into consideration:

(1) Check the measurement of your variables both the independent and confounding variables;

(2) Carefully check the measurement of your dependent variable as well;

(3) Include more control variables and make sure that their measurements is in ratio not binary digit;

(4) Consider increasing the sample size of the study;

(5) Ensure proper cleaning/proof-reading of your data prior to running the results;

(6) Ensure appropriate use of estimation technique that best suit your data;

(7) Conduct advanced estimation tests in order to address issues related to the violation of the 11 assumptions for Best Linear Unbiased Estimator (BLUE) as advocated by Gujarati Damodar. For instance, the multicollinearity problem, the negative Adjusted R2, and Poor model fitness value encountered were among the violations of the classical linear regression assumptions.

I am optimistic that a very good regression results can be obtained if the aforementioned points have been properly taken into considerations.

Best Regards,

Dr. Yusuf Ja'afar [PhD Accounting & Finance - Nigeria]

Yusuf Ja'afar , I think you are using the term "spurious" incorrectly. A spurious relationship would have a large r-square --- or large enough that it looks like a meaningful relationship.

Thanks all for your answer. I was wondering about robust regression; if I see any significant or a too-positive low adjusted R square close to zero, can I report robust regression instead of linear regression?

I think robust regression is the alternative for OLS when there are outliers.

Any input is appreciated.