Question

Question: Write a first-order model relating to

1. Two quantitative independent variables.
2. Four quantitative independent variables.
3. Five quantitative independent variables.

Short answer

Answer

$$\begin{gathered} \mathit{a}\mathbf{.}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}} \\ \mathit{b}\mathbf{.}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathit{\beta }}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{4}} \\ \mathbf{c}\mathbf{.}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathbf{x}}_3\mathbf{+}{\mathit{\beta }}_{\mathbf{4}}{\mathbf{x}}_4\mathbf{+}{\mathit{\beta }}_{\mathbf{5}}{\mathbf{x}}_5 \end{gathered}$$

Step-by-step solution

First order model

A first order model relating to 2 quantitative independent variables will involve 2 quantitative variables x₁ and x₂which are independent variables.

Thus, a first order model with 2 quantitative variables is$\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}$.

First order model

A first order model can be written as follows:

A first order model relating to 4 quantitative independent variables will involve 4 quantitative variables x₁ ,x_{2 ,}x₃and x₄ which are independent variables.

Thus, a first order model with 4 quantitative variables is$\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathit{\beta }}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{4}}$.

First order model

A first order model can be written as follows:

A first order model relating to 5 quantitative independent variables will involve 2 quantitative variablesx₁ ,x_{2 ,}x₃x₄ and x₅which are independent variables.

Thus, a first order model with 2 quantitative variables is$\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathbf{x}}_3\mathbf{+}{\mathit{\beta }}_{\mathbf{4}}{\mathbf{x}}_4\mathbf{+}{\mathit{\beta }}_{\mathbf{5}}{\mathbf{x}}_5$.