In a simple regression analysis, calculating the p-value from the F- or from the t-statistic is equivalent (t² = F, the p-value should be the same).

Thank you @jochen

The f cal was greater than the f value. But the p value was statistically significant. Can I report that p value with out the f ?

I think you mean the F of the residuals as a model fit indicator, not the F showing the effect of your variable.

Jochen Wilhelm

Is t2 =f true at all degrees of freedom, or merely DF=1?

Best

Seyyed Amir Yasin Ahmadi ,

I assume we are talking about a simple regression, i.e. there is one single predictor in the model, and the "significant p-value" is for the coefficient of this predictor (otherwise, the interpretation of the p-value taken out of a more complex multiple reegression model would not be very sensible).

In such a simple regression, the squared t-value for the coefficient is identical to the F-value of the overall model. If there are n data points observed, the t-value is compared to a t-distribution with n-2 d.f. (tn-2), and the F-value is compared to the F-distribution with 1 and n-2 d.f (F1,n-2).

Formally: if t ~ tν the t² ~ F1,ν

If the regression k predictors, the model F is compared to Fk,ν. For k > 1, this is not identical to t².

Again, the question of Mumin Olatunji Oladipo makes sense only if the mentioned p refers to the sole predictor in the model. If there are other predictors, the meaning of this p may not at all be clear (it depends on the precise structure of the model and the theory), and simply comparing a model-p to a predictor-p is nonsense (it's comparing apples and peaches, so to say).

Mumin Olatunji Oladipo

Could you please upload a screenshot from your software?

Here is the regression analysis result.

Mumin Olatunji Oladipo , thank you for showing the results. But they don't fit to your question... the p-values are both identical (2.09E-10).

Note to Seyyed Amir Yasin Ahmadi : F = 85.2 = t² = 9.23².

Jochen Wilhelm is right

It is a simple regression and also the single variable is continuous (as I remember DF is 1 for 2 groups and for continuous variables). Therefore P(F) = P(t) here.

There is no problem.

Thanks Mumin Olatunji Oladipo & Jochen Wilhelm

Thank you both @Jochen Wilhelm and @Amir.

Does it mean I can report this result has been statistically significant?

Yes.