I have a classic linear model, with 5 possible regressors. They are uncorrelated with one another, and have quite low correlation with the response. I have arrived at a model where 3 of the regressors have significant coefficients for their t statistic (p<0.05). Adding either or both of the remaining 2 variables gives p values >0.05 for the t statistic, for the added variables. This leads me to believe the 3 variable model is "best".
However, using the anova(a,b) command in R where a is the 3 variable model and b is the full model, the p value for the F statistic is < 0.05, which tells me to prefer the full model over the 3 variable model. How can I reconcile these apparent contradictions ?
Thanks PS Edit: Some further background. This is homework so I won't post details, but we are not given details of what the regressors represent - they are just numbered 1 to 5. We are asked to "derive an appropriate model, giving justification".