studying with a factor model, I get confused more and more as I think about factor exposure and factor return
The concept (or mechanism) I get used to is evaluating a factor's Long Short Return(Q1-Q5) and see whether it gives us statistically significant return by checking t-stat. If t-stat turns out to be valid, then I'm free to use that factor. (Below picture is the one I get used to regarding to factor)
However, in the factor equation "r=Bf+s" I'm not sure where the procedure above takes into account. Does factor return "f" mean the Q1-Q5 long short return? Moreover, there are roughly 3 types of risk factors. fundamental factor, macroeconomic factor and statistical factor. I think fundamental factor like value factor or quality factor can be used to calculate long short return because every single stock has a factor data related to value or quality. However how can I adopt such long short return evaluation mechanism in macroeconomic factor? If I have to estimate every asset's beta related to a certain macroeconomic factor through linear regression, where does the long short return procedure kicks in?