F statistics aren't of the model but rather of the estimation method, ordinary least squares. In quantile regression, the estimation method is not ordinary least squares.
I do agree with David Eugene Booth . You will find F value in case you are running least square equation model of regression. SPSS will give you the F value and its significance on running regression
am having similar problem though mine is how to calculate goodness of fit ( R - square) for .10,.25, .75 and .90. unfortunately one of the quantiles keep given me more than a unit value. what should i do