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Why does AIC and BIC disagree?
As you know, AIC and BIC are both penalized-likelihood criteria. But despite various subtle theoretical differences, their only difference in practice is the size of the penalty; BIC penalizes model complexity more heavily. The only way they should disagree is when AIC chooses a larger model than BIC.
What is the null hypothesis for the F-test?
The F-test for overall significance has the following two hypotheses: The null hypothesis states that the model with no independent variables fits the data as well as your model. The alternative hypothesis says that your model fits the data better than the intercept-only model.
What does a high AIC score mean?
Since the AIC scales linearly with the number of parameters it is easily possible to get a high AIC score. The difference in the AIC scores for two different models can be interpreted as ‘extra information lost’ by using the worse model in comparison to the better model.
How to interpret the F-test of overall significance in?
Typically, you don’t interpret the F-value directly, but instead the p-value associated with it. For the F-test, your p-value of 0.000 indicates the model as a whole is statistically significant. Additionally, it looks like your independent variables are also significant. The R-squared is also high. It looks like good results overall.
Is it normal to have significant F-test but insignificant variable?
So, it’s not surprising to have a significant overall F-test but an insignificant variable (or even more than one). Regarding the model with the insignificant independent variable, you’ll have to use a mix of statistics and theory to determine whether to leave that variable in the model.
How does the F-test determine if all predictor variables are jointly significant?
Thus, the F-test determines whether or not all of the predictor variables are jointly significant. It’s possible that each predictor variable is not significant and yet the F-test says that all of the predictor variables combined are jointly significant.
Is the F-test a formal statistical test?
Although R-squared can give you an idea of how strongly associated the predictor variables are with the response variable, it doesn’t provide a formal statistical test for this relationship. This is why the F-Test is useful since it is a formal statistical test.