Using a chi square test instead of a F test in a linear regression I'm reading a paper where the statistic reported for testing the general significance of a multiple linear regression is a "Wald Chi Square" instead of the usual "F" statistic.
Is it the same thing to use the Chi Square statistic or the F statistic or in what occasions are the two used?
 A: They are closely related. If you divide the Wald statistic by its degrees of freedom, you in essence have an $F$ statistic with that many numerator df, and infinite denominator df. The Wald statistic is seen in cases where the error variance is known, or where asymptotic (large-sample) approximations are used. Seems surprising to see it in a linear regression, as usually there you have a mean-square-error term and use that to make an $F$ test. But in generalized linear models, like logistic or Poisson regression, they are pretty common.
A: This is analogous to the $z$-test vs the $t$-test in the univariate case, where if the variance is known, the distribution of the test statistic is normal ($z$-test), and if it is estimated, the distribution of the test statistic is $t$ ($t$-test), with the $t$-test converging to the $z$-test with large n.
Same thing in linear regression, if the error variance is assumed known (or large $n$ with the asymptotic assumption), then wald test. You are correct that the p-value based on the $F$ is usually reported. 
In addition, note that the wald chi-square test reduces to the $z$-test with one variable, and that the $F$-test reduces to the $t$-test.
A wrinkle here - another test that uses the chi-squared distribution is the likelihood ratio test, though I don't think I've seen it referred to as a wald test before.
