Question

• Which regression coefficients (unstandardized or standardized) do you compare to determine the most important predictor variable in the model? Comparing these regression coefficients, would you compare the regression coefficients of all of the predictor variables in the model or just the regression coefficients of the significant predictor variables? After comparing the regression coefficients, how do you know which of the predictor variables is most important?

Answer 1

Unstandardized regression coefficients describes the relationship between predictor variable and response variable. That coefficient represents the mean change in the response for one unit increase in the predictor. For different variables corresponding units are also different. Hence direct comparison of these coefficients do not give valuable information. Also we can see that if we fit one model using weight in grams and another model using weight in kilograms then the coefficients show large change. That is why we use standardized regression coefficients.

Standardization involves subtracting the variable's means from each other and then dividing by standard deviation. Then we can fit the regression model using these standardized coefficients and compare the coefficients for identifying which of the predictor variable is most important, because all the coefficients have same scale. Then identify the predictor variable that has the largest absolute value for it's standardized coefficients. That variable is the most important predictor variable.