Given below are the alternative formulae for F-test statistics. We are interested in testing the statistical significance of the incremental contribution of X3 at 5% level of significance to Y = β0 + β1X1 + β2X2 + U. Which of these is not appropriate? Where RSS is residual sum of square and ESS is explained sum of square.
1
\(\rm F=\frac{R^2_{UR}-R^2_R/d.f.}{(1-R^2_{UR})/d.f.}\)
2
\(\rm F=\frac{ESS/d.f.}{RSS/d.f.}\)
3
\(\rm F=\frac{ESS_{new}-ESS_{old}/d.f.}{ESS_{new}/d.f.}\)
4
\(\rm F=\frac{R^2/d.f.}{(1-R^2)/d.f.}\)