Question

Consider relating E(y) to two quantitative independent variables x₁ and x₂.

1. Write a first-order model for E(y).
2. Write a complete second-order model for E(y).

Short answer

1. A first-order model for E(y) with two quantitative variables x₁and x₂ can be written as$E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\epsilon$.
2. A Second-order model for E(y) with two quantitative variables x₁and x₂ can be written as$E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x_1}^2+{\beta }_4{x_2}^2+\epsilon$ .

Step-by-step solution

First-order model for E(y)

A first-order model for E(y) with two quantitative variables x₁and x₂ can be written as $E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\epsilon$.

Second-order model for E(y)

A Second-order model for E(y) with two quantitative variables x₁and x₂ can be written as $E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x_1}^2+{\beta }_4{x_2}^2+\epsilon$.