As i am working on multiple regression models (quadratic equations). by using backward elimination method. i have removed the insignificant terms in the model and reconstruct the equation by using only significant terms. is it right to do like this. to define the relation between the dependent and independent variables.
example: out of 9 independent terms, 3 terms are not significant, so remove that insignificant terms and once again develop a new equation using remaining 6 terms.
Yes it is acceptable to remove nonsignificant independent variables and reconstruct the multiple regression model. This new (subset) model is bound to be more adequate than the former. For instance it will have a higher R squared. That is, more variation of the data is accounted for by the model, irrelevant variables having been removed.
Dear Mr. Vijay Kumar,
You can remove the non contributory IVs in ascertaining the dependent variable, and it only strengthens the model fit.
yes, it is possible, but i still advise you to go through the discussion on polynomial regression models in the relevant chapter of the Regression analysis book by Draper and Smith for more insight and in depth discussion of this problem.
Vijay Kumar Shankar You are absolutely right to have removed the non-significant IVs.
Not necessarily. The variables function together, and what you want is the best set of variables which produce the best predicted-y values, if you are most interested in prediction. You could be more interested in explanation and may want to consider the following:
https://www.researchgate.net/publication/48178170_To_Explain_or_to_Predict. The appendix has an informative example. But you still have to consider how variables influence one another through collinearity and other means. If you check ResearchGate now you will see that there are people arguing against forward or backward elimination as not likely finding the best set of variables, depending on the order of selection. And if you then go by "significance" you may find that because the variables you do have at that point also influence one another, the "significance" of each remaining variable will change. You can research "model selection" techniques, but keep in mind your subject matter knowledge, which may help you decide on which variables, working together, will provide the needed information. Keep in mind that adding unneeded variables tends to increase variance, and leaving out needed ones can result in omitted variable bias. Results can change for different samples, so consider both a "graphical residual analysis," and a "cross-validation." A graphical residual analysis is for a single sample, and though results vary by sample, they are very informative. Also note that if you have the best set of variables used in the best function, you increase your chance of "essential heteroscedasticity," which is a feature, not a bug, which says that a larger predicted value should be associated with an increase in sigma for the residuals. - Cheers all.
Il possible de faire de sorte que le logiciel retir automatiquement les variables non significatives en les éliminant une après l'autre. Cela est possible dans R ou python.
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