The adjusted r-square is a standardized indicator of r-square, adjusting for the number of predictor variables. This shows the standardized variance of the independent variables on the dependent variable in regression analysis. The adjusted r-square includes the degrees of freedom for the statistical model, which is the total number of variables minus one.
The more predictor variables in the model, the larger the variance between each variable. A predictor variable is an aspect or condition the researcher believes shares a relationship with the outcome of a study. There is an increase in the adjusted r-square from the r-square when the additional predictor variables make the model a better fit. Adjusted r-square is a ratio on a scale from zero to one.
Researchers use the adjusted r-square to test the strength of the model. It is also an indicator of which variables to include in a data model. If the researcher removes one variable and the adjusted r-square increases, the researcher knows there is a problem with that variable. In a strong statistical model, the adjusted r-square is higher than the r-square. Texas University explains that a low adjusted r-square suggests a model issue with applying the results of the study to the general population. This problem arises when the solution includes too many independent variables. This process is also useful to form an analysis of variance in statistics.