Dummy variable question in regression

#1
Hello,

I'm trying to understand dummy variables in regression. I'm regressing the price of diamonds against (1) weight (2) Clarity and (3) Colour. Clarity and colour and dummy variables and I created these in Minitab. This is the equation.

Price = 1.65 Weight + 3.99 Clarity_A + 3.86 Clarity_B + 0.210 Colour_A
+ 0.157 Colour_B

Is the Price for a weight = 2, Clarity A and Colour B the following?

Price = 1.65(2) + 3.99(1) + 3.86(0) + .210(0) + .157(1)
Price = 5.797

Thank you
 
#2
Yes it is correct, but only if:

- clarity and colour both have only 2 options (A and B)

What I mean is, if for instance clarity and colour be A, B and C, then you need to include a constant in your model. But given your information, it is correct.

(Ofcourse, only if all assumptions of OLS are satisfied)
 
#3
Either color or clarity (or both) has to have more than two levels, else the design matrix would have linear dependence (even w/o an intercept).