Question

It is desired to relate E(y) to a quantitative variable x₁ and a qualitative variable at three levels.

1. Write a first-order model.
2. Write a model that will graph as three different second- order curves—one for each level of the qualitative variable.

Short answer

1. A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written as $E\left(y\right)={\beta }_0+{\beta }_1{x}_x+{\beta }_2{x}_x+{\beta }_3{x}_3$.
2. Graph

Step-by-step solution

First-order model

A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written as$E\left(y\right)={\beta }_0+{\beta }_1{x}_x+{\beta }_2{x}_x+{\beta }_3{x}_3$,

Where x₁ is the quantitative variable

And x₂ and x­₃ represent level 1 and level 2 of the qualitative variable.

Graph