Chapter 12: Q.67E (page 755)

Question: Write a regression model relating E(y) to a qualitative independent variable that can assume three levels. Interpret all the terms in the model.

Short Answer

Expert verified

Answer:

The regression model for one qualitative independent variable with two-level is $E (y) = β_{0} + β_{1} x_{1} + β_{2} x_{2} + β_{3} x_{3}$ .Here $β_{0}$ denotes $μ x i$ the mean for base level and role="math" localid="1649848834273" $β_{1}, β_{2}$ _, and $β_{3}$ denotes the difference between the mean levels for different dummy variables. While, $x_{1}, x_{2}$ , and $x_{3}$ denotes the dummy variables used in the model which can take the value of either 0 or 1.

Step by step solution

Regression model for one qualitative independent variable

A regression model relating the mean value of y to a qualitative independent variable that can assume two levels can be written as

$E (y) = β_{0} + β_{1} x_{1} + β_{2} x_{2} + β_{3} x_{3}$

Where, $x_{1}$ is the dummy variable for $i+1level$

Meaning $x_{1} = (\begin{matrix} 1 i f y i s o b s e r v e d a t l e v e l i + 1 \\ 0 0 t h e r w i s e \end{matrix})$

Interpretation of the terms in the model

Here $β_{0}$ denotes $μ x i$ the mean for base level and _{$β_{1}, β_{2}$} and $β_{3}$ denotes the difference between the mean levels for different dummy variables. While, $x_{1}, x_{2}$ , and $x_{3}$ denotes the dummy variables used in the model which can take the value of either 0 or 1.