This post is a continuation of my previous post.

After reading all comments and answer, I think that F-statistics tells us whether explanatory variables in a model is significant or not, as the null hypothesis in F-test is that the variables have no predictive power.

As model 2 has unusually high F-statistics compared to model 1, am I right to say that model 2 is kind of 'weird'?

Also, what does more negative F-statistic imply? Does it have smaller or larger p-value?


the null hypothesis in F-test is that the variables have no predictive power

This is an incorrect understanding. The null hypothesis for an F test of nested models is that the encompassing model does not explain more variance than the smaller encompassed model, except for fitting noise. The F test is not about predictive power at all.

F statistics are hard to interpret without knowing the degrees of freedom. Given that your table notes "coefficients", it appears like all your predictors are numerical, rather than, say, categorical. In this case, one can say that the larger F value for model 2 than for model 1 indicates that the improvement that model 2 offers over the intercept-only model is larger than the improvement that model 1 offers over the intercept-only model - in both cases, in terms of variance explained. One can hope (hope!) that this means that model 2 will yield better predictions, but this is not at all clear-cut.

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  • $\begingroup$ It seems that from my lecturer's note, degree of freedom is the number of explanatory variables (exclude constant). $\endgroup$ – Idonknow Sep 11 '19 at 0:22
  • $\begingroup$ An F distribution has two degrees of freedom (numerator d.f. and denominator d.f.) $\endgroup$ – Glen_b Sep 11 '19 at 2:44
  • $\begingroup$ My bad. I forgot to include another df: number of explanatory variables and 100 - number of explanatory variable - 1 (for constant term). $\endgroup$ – Idonknow Sep 11 '19 at 5:59

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