Consider the model:
y = β0 + β1x1 + β2x2 + β3x3 + ε
where x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme

The resulting least squares prediction equation is
= 44.8 + 2.2x1 + 9.4x2 + 15.6x3
a. What is the response line (equation) for E(y) when x2 = x3 = 0? When x2 = 1 and x3 = 0? When x2 = 0 and *3 = 1?
b. What is the least squares prediction equation associated with level 1? Level 2? Level 3? Plot these on the same graph.

if level 2 otherwise 1 if level 3 0 otherwise 1 2