You want the model with the best performance. If you split your data to see how well one part predicts for the other, you could compare various full model performances that way.
Scatterplot graphics can give you a great deal of insight. You might try scatterplots of y with predicted y on the x-axis for each full model. You could also compare regressors (predictors), but note that there could be important interactions between regressors. You may be able to find collinearities. At any rate, experimenting with scatterplots could be useful.
Cheers - Jim
Article Practical Interpretation of Hypothesis Tests - letter to the...
Dr. Knaub has given some good suggestions. You might also try variable selection by lasso or elastic net(at the moment I prefer lasso). For easy to use code,see the links below. Best wishes
Any model selection based on statistical measures of the observed data is problematic. They are not more than a crutch for the case that one has not enough knowledge about the subject to judge the relevane of the variables (what happens, in fact - as often in science, so it may be one of "the best things possible", but this does not make it become a good solution; it remains a crutch yet).
At the end it is *your decision* what variables to keep and what variables to ignore. If you justify your decisions on p-values then you should be able to explain or give arguments why you did so and why you have chosen your selection level (be it 0.05 or 02 or anything else! It does not matter! You should always be able to give some subject-matter reason for your choice! - again most people silently ignore it and claim that 0.05 is a common standard, what is fact, but what is silly, too). The best is to give the arguments directly. If you think that some variable should be in the model, for reasons based on the subject matter, then keep it. If you think it is not relevant, then remove it.
You should further keep in mind that variables can adjust the effects of other variables in the model, even if they do not have any low p-value themselves. The question is whether or not you like to consider this (possible) adjustment.
thank you all .. im reading through it . i have not fully understood what you all have said as my experience with statistics is pretty low. im still a rookie in it.