Can we interpret the negative adjusted r square in linear regression model summary.

[Deepa Ahuja]

Respected all  community members. 

In  linear regression model summary, 

R is  0.035 

R square is 0.001 and 

Adjusted R square is   -0. 001 

With p value of 0.480 

My concern here is negative adjusted r square. 

Can we or shall we can report the negative r sqaure.

Can i interpret that Model here shows extremely weak relationship and the result as non significant.

Or something is need to be done to improve the value of adjusted r square. ? 

Regards 

Deepa ahuja 

[Sunil PICTC]

Can we interpret the negative adjusted r square in linear regression model summary.

Sir,

Number of Independent variables in the model are adjusted by adjusted  R Square as it increases by adding the variable improving the model.

Negative Adjusted R2 means that the variation in the values predicted by model is more than the variation around mean of sample indicating that the mean value is better than prediction.

It seems that you have too many independent variables and sample size is small. Your model may be having some avoidable independent variables,  not  relevant to your study.

You may need to increase the number of records and reselect the independent variables and  check for collinearity issues.

Since adjusted R² is less than 0, it means R-Squared value is less that k / (n-1)  [k = number of IV and n = number of records] . Therefore, for adjusted R²  to be positive, you need to have R² more than k/(n-1)

Other Respected Members may also be willing to share their views also.

Regards

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[Sunil PICTC]

Negative Adjusted R2 means that the sample mean value is better than model prediction.