How to do significance test of △R2 and △F?

[Zexu Li]

How to do significance test of △R² and △F?

Dear all:

I have two models (nested model)to regress like follows:

xtreg y x1 x2, fe
xtreg y x1 x2 x3, fe

from these two nest model, I can get R² and F of each model , also I can easily get △R² and △F.
But How can I do significance test of △R² and △F? and show the results like △R²=0.16** and △F=3.456*

Some people told me the way like follows：

reg y x1 x2
est store a
reg y x1 x2 x3
est store b
ftest a b

Yes ,I can get F value, but I feel that it is not the significance test of △R² and △F I want.

[Clyde Schechter]

There is no official Stata command -ftest-. If it is a user-written command you are asked to say so and indicate where it can be found.

In any case, there are a few different ways to do this, provided that the estimation samples for both regressions are the same. If the inclusion of the additional variable x3 results in a smaller estimation sample due to missing values in x3, then you cannot do this test at all, and any formula that you think is working is just giving you nonsense.

But assuming the estimation sample remains constant, the simplest way is to just look at the output table from the second regression, specifically at the row for x3 itself. The t-statistic for x3 is the square root of the F-statistic for the change in R², and the p-value for the F-test is exactly the same as the p-value shown for that t-test. The F-statistic for the change has 1 numerator degree of freedom, and its denominator degrees of freedom is the same as that of the F statistic for the overall second regression.

[Zexu Li]

Thank you very much for your reply.

I read it carefully and check your answers with data.

I found that you are absolute right. The F value I get from ftest is just the square value of t-statistic for x3 .
Consider the ftest can not be uesd in panel data ,so your answer can be uesd more widely.

Thank you very much .Wish you have a good day.