What does WLS do? How useful are F stats and t stats here?

WLS stands for weighted least-squares, which is an alternative to standard least-squares regression. It assigns weights to data points when performing the regression so that points with more influence are given greater emphasis. The F statistic and t statistic are useful for determining the significance of the regression in WLS; in particular, the F statistic can be used to test the overall significance of the regression, whereas the t statistic can be used to test the significance of individual variables.