Omnibus Tests in Multiple Regression
In Multiple Regression the omnibus test is an ANOVA F test on all the coefficients, that is equivalent to the multiple correlations R Square F test. The omnibus F test is an overall test that examines model fit, thus rejecting the null hypothesis implies that the suggested linear model is not significally suitable to the data. In other words, none of the independent variables has explored as significant in explaining the dependant variable variation. These hypotheses examine model fit of the most common model: yi=β0 + β1 xi1 + ... +βk xik + εij
estimated by E(yi|xi1....xik)=β0+β1xi1+...+βkxik ,where E(yi|xi1....xik) is the dependant variable explanatory for the i-th observation, xij is the j-th independent (explanatory) variable, βj is the j-th coefficient of xij and indicates its influence on the dependant variable y upon its partial correlation with y. The F statistics of the omnibus test is:
Whereas, ȳ is the overall sample mean for yi, ŷi is the regression estimated mean for specific set of k independent (explanatory) variables and n is the sample size.
The F statistic is distributed F (k,n-k-1),(α) under assuming of null hypothesis and normality assumption.
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