Question about dummy variables

Hi Guys,
So I am doing a project for a class, and had a question on how to interpret something on my SPSS. I am designing a multivariate regression model that looks at price (dependent variable) based on multiple predictors, including brand, which I dummy coded with, say, brand E as my reference variable. When I made a correlation table for these variables, I can easily see the Pearson correlation for brands A-D to the price. However, what if I wanted to know how brand E correlates to price? Would I have to go back and recode my dummy variables so that my reference variable is brand A instead? I understand that technically the info for brand E is in my table, as the correlations of brands A-D are based relative to brand E. Also, I get that in my multiple regression equation for this, the coefficients for brands A-D are telling me the difference in mean price compared to brand E, when all else is constant. Can anyone provide help with explaining this to me? This is a very new subject to me, but I can already see how understanding how to do this is very useful, and want to make sure I understand it. Thanks!