91Ó°ÊÓ

A first-order model equation in one quantitative variable which is solicitor’s beauty rating here (say x₁) and one qualitative variable which is solicitors’ hair color here with 3 levels (say variables introduced are (k-1) = 2;x₂and x₃) can be written as${\mathbf{\text{·¡(²â)=β}}}_{\mathbf{0}}\mathbf{\text{+}}{\mathit{β}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{β}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{β}}_{\mathbf{3}}{\mathit{x}}_{\mathbf{3}}$

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Assume thatx₂= solicitors’ hair color is blond Caucasian and x₃= solicitors’ hair color is brunette Caucasian

The base level for hair is assumed to be minority female.

Therefore, for minority female the 1-point increase in solicitor’s beauty rating will be represented by${\mathit{β}}_{\mathbf{1}}$

For blond Caucasian hair color of the solicitor, the 1-point increase in solicitor’s beauty rating will be represented by$\mathbf{(}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{2}}\mathbf{)}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}$

For brunette Caucasian hair color of the solicitor, the 1-point increase in solicitor’s beauty rating will be represented by$\mathbf{(}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{3}}\mathbf{)}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}$

An interaction model for mean contribution level, E(y) as a function of a solicitor’s hair color and beauty rating can be written as$\mathbf{E}\mathbf{\left(}\mathbf{y}\mathbf{\right)}\mathbf{=}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{β}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{β}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathbf{β}}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{β}}_{\mathbf{5}}{\mathbf{x}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{3}}$

Assume that x₂ = solicitors’ hair color is blond Caucasian and x₃= solicitors’ hair color is Brunette Caucasian

The base level for hair is assumed to be minority female.

Therefore, for minority female the 1-point increase in solicitor’s beauty rating will be represented by${\mathbf{β}}_{\mathbf{1}}$

For blond Caucasian hair color of the solicitor, the 1-point increase in solicitor’s beauty rating will be represented by$\mathbf{(}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{2}}\mathbf{)}\mathbf{+}\mathbf{(}{\mathbf{β}}_{\mathbf{1}}\mathbf{+}{\mathbf{β}}_4\mathbf{)}{\mathbf{x}}_{\mathbf{1}}$

For brunette Caucasian hair color of the solicitor, the 1-point increase in solicitor’s beauty rating will be represented byrole="math" localid="1651143179432" $\mathbf{(}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{3}}\mathbf{)}\mathbf{+}\mathbf{(}{\mathbf{β}}_{\mathbf{1}}\mathbf{+}{\mathbf{β}}_5\mathbf{)}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}$