Question

Write a model relating E(y) to one qualitative independent variable that is at four levels. Define all the terms in your model.

Short answer

Mathematically, the model in one qualitative independent variable with 4 levels can be written as $E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3$

Step-by-step solution

A qualitative model

A model relating E(y) to one qualitative independent variable with 4 levels can be written by introducing (k-1) variables in the model to define the 4 different levels where 3 variables define 3 levels when the value of a particular variable is 1 and one level is defined as base level when all variables are 0.

4 levels

Mathematically, the model can be written as$E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3$

Where x1= 1, if level 1 is present; otherwise 0

X₂= 1, if level 2 is present; otherwise 0

X₃ = 1, if level 3 is present; otherwise 0