91Ó°ÊÓ

a. A first-order model with one quantitative independent variable can be written as $\mathbf{E}\mathbf{\left(}\mathbf{y}\mathbf{\right)}\mathbf{=}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}$.

b. A model including both quantitative and qualitative variables with 3 levels can be written as $\mathbf{E}\mathbf{\left(}\mathbf{y}\mathbf{\right)}\mathbf{=}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{β}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{β}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}$.

c. A model including both qualitative and quantitative variables with interactions can be written as $\mathbf{E}\mathbf{\left(}\mathbf{y}\mathbf{\right)}\mathbf{=}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}\mathbf{x}{}_{\mathbf{1}}\mathbf{+}{\mathbf{β}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{β}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathbf{β}}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}\mathbf{β}{}_{\mathbf{5}}{\mathbf{x}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{3}}$.

d. The response lines of the model in part c will only be parallel if no interaction amongst the variables is observed in the model. If there’s any interaction amongst the variables, then the response lines will be intersecting each other.

e. The model in part c will have only one response line when there’s no interaction in the model and the y-intercepts and slope values for all the variables are the same.