According to the algorithm for the backward stepwise selection from the book ISLR which is shown below:
says that we need to choose the model among the $k$ models by having a smallest RSS or highest $R^{2}$, while other resources tells that for choosing the predictor/s to be included in the model based on their $p$-values as stated here.
Can someone tell what is the right process?
These are two different methods, each with advantages and disadvantages.
The method in ISLR is more computationally intensive. It fits 1+p(p+1)/2 models, where p is the number of predictors. The other backward selection method fits at most p+1 models.
On the other hand, the method in ISLR is more statistically sound. In general, the practice of comparing p-values to each other is frowned upon by statisticians. See principle number 5 in the ASA's Statement on p-Values: https://www.tandfonline.com/doi/pdf/10.1080/00031305.2016.1154108?needAccess=true
