Methods to determine the important predictor in an OLS regression model

This is a very subjective issue. A variable might be important in one situation but not in the other. It depends on the subject area and goals. For another, how you collect and measure your sample data can influence the apparent importance of each variable. But somehow I will try to explain those techniques to identify the strongest variable, keeping this in mind.

First of all, I will make you know what are those things which you should not use to compare the importance of a variable.

a)   Regression Coefficients: Larger coefficients don’t necessarily identify more strong predictor variables because of the fact that there are different units within each type of measurement.

b) P-values: Low p-values don’t necessarily identify predictor variables that are practically important because  A statistically significant result may not be practically significant.

Do Compare These Statistics To Help Determine the strongest Variable

Statistical Methods,

a) Standardized regression coefficients: I have explained above how regular regression coefficients use different scales and you can’t compare them directly. However, if you standardize the regression coefficients so they’re based on the same scale, you can compare them. Look for the predictor variable with the largest absolute value for the standardized coefficient.

b) Change in R-squared when the variable is added to the model last: Because the change in R-squared analysis treats each variable as the last one entered into the model, the change represents the percentage of the variance a variable explains that the other variables in the model cannot explain. In other words, this change in R-squared represents the amount of unique variance that each variable explains above and beyond the other variables in the model.

Non-Statistical Considerations: Statistical measures can show the relative importance of the different predictor variables. However, these measures can't determine whether the variables are important in a practical sense. To determine practical importance, you'll need to use your subject area knowledge.

Also, how you collect and measure your sample can bias the apparent importance of the variables in your sample compared to their true importance in the population. If you randomly sample your observations, the variability of the predictor values in your sample likely reflects the variability in the population. In this case, the standardized coefficients and the change in R-squared values are likely to reflect their population values.

So, besides all the statistical measures, you have to use your expertise to determine which variable is an important and strong predictor.

Thanks