Consider the model
y = β0 + β1x1 + β2x2 + β3x3 + Ɛ
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
ŷ = 44.8 + 22x1 + 9.4x2 + 15.6x3
What is the response line (equation) for E(y) when x2 = x3 = 0? When x2 = 1 and x3 = 0? When x2 = 0 and x3 = 1?
b. What is the least squares prediction equation associated with level 1? Level| 2? Level |3? Plot these on the same graph.

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[1 if level 2 otherwise S1 if level 3 lo otherwise X2 X3