Suppose the analyst now adds four more independent variables to the regression, and the R2 increases to 65%. Identify which model the analyst would most likely prefer.
Before adding, R2: 63%, adjusted R2: 59.6%
After adding, R2: 65%, adjusted R2: 58.7%
Answer: The analyst would prefer the first model because the adjusted R2 is higher and the model has five independent variables as opposed to nine.
I am wondering what’s the condition of preference one over another? Just higher adjusted R2 is a better measure?
You want the simplest possible model that explains whatever you are working with adequately. the R squared is one way to measure how well the equation explains the data, but it is flawed in the sense that the more variable you add, the more R squared increases, even if the additional variable adds very little additional information. adjusted R-squared was developed to work around this flaw: it adds a penalty for every additional variable you add. if the variable adds significant more information, adjusted R squared increases. if, however, it doesn’t add much additional information, adjusted R squared decreases.
You want the model with the largest adjusted R squared, which has the least amount of variables that explains the data well enough.