I have a dataset with 25 observations. The variables are y, k and l.
I run the following regression
regress y k l
I want to test that the parameters on k and l sum to 10
I type:

test k+l=10

( 1) k + l = 10

F( 1, 22) = 107.68
Prob > F = 0.0000

.
My issue is that when I create the restricted regression and calculate the F-statistic using the usual formula ((R2unrestricted-R2restricted)/q)/((1-R2unrestricted)/(n-k)) I get a much smaller number...still rejecting the null hypothesis

my restricted model is y-10L=B0+B1(k-l)+E
. gen Y_10L = y-10*l

. gen k_l=k-l

. regress Y_10L k_l

and I don't get a number that is equal to 107, I get around 47 using the above formula.

I am just curious about what is going on. Is it a sample size issue?



My data is here:


* Example generated by -dataex-. To install: ssc install dataex
clear
input float(y k l)
68.24103 9.313 45.0961
69.15226 10.6264 43.9693
70.05865 11.5423 41.8166
79.74423 11.9624 44.4985
89.43562 12.2972 48.7602
93.72334 13.045 51.1402
102.4281 13.6777 54.4577
95.21549 14.2198 51.2944
108.347 14.7225 54.0984
108.1351 15.1736 55.7854
107.1986 16.0311 55.9122
100.4691 16.8214 52.6973
109.6668 16.9557 56.4288
115.2529 16.9042 56.9827
116.6837 17.1108 56.0163
129.3971 17.2227 58.5997
132.359 17.4505 59.6128
147.1149 17.8079 61.1658
159.5804 18.4595 64.6947
173.8529 19.6165 69.2726
175.291 21.2163 70.161
184.5142 22.4894 72.3024
196.5472 23.5281 74.2756
183.8358 24.7325 71.2039
177.0066 25.6062 68.9305
end
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