I'm studying the variation of cost of the same procedure (specifically, the total cost of disposable items used for stone laser surgery, aka ureteroscopy with laser lithotripsy) across different hospital sites and surgeons. My dataset contains information from 8 surgeons and 6 sites. My 1st hypothesis is that the site and surgeon predict cost, e.g., surgeon #1 may prefer a more expensive device, or site #3 may have only the cheaper item in their inventory. My 2nd hypothesis is that site is the more dominant (or is even confounding) the effect of the surgeon, since the surgeon may not get much say if the site's inventory doesn't carry the item the surgeon prefers to use.

So, I have two categorical independent variables (surgeons #1-8, sites #1-6), and a continuous dependent variable (total case cost in $$). I know that I could model this with linear regression using dummy variables for all iterations of the categorical predictors, or could use ANOVA, but I'm not sure which test is more appropriate. Thanks