Chapter 12: Q.66E (page 755)

Question: Write a regression model relating the mean value of y to a qualitative independent variable that can assume two levels. Interpret all the terms in the model.

Short Answer

Expert verified

Answer:

Regression model for one qualitative independent variable with two level is $x_{1} = (\begin{matrix} 1 I F y i s o b s e r v e d a t l e v e l i + 1 \\ 0 o t h e r w i s e \end{matrix})$ .Here $β_{0}$ denotes $μ x i$ the mean for base level $β_{1}$ and $β_{2}$ denotes difference between the mean levels for different dummy variables. While, $x_{1}$ and $x_{2}$ denotes different levels of dummy variables used in the model which can take 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

$E (y) = β_{0} + β_{1} x + β_{2} x^{2}$

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

Meaning $x_{1} = (\begin{matrix} 1 IF y is observed at level i + 1 \\ 0 otherwise \end{matrix})$

Interpretation of the terms in the model

Here $β_{0}$ denotesrole="math" localid="1649848061325" $μ x i$ the mean for base level

$β_{1}$ and $β_{2}$ denotes difference between the mean levels for different dummy variables.

While,role="math" localid="1649848167521" $x_{1}$ and role="math" localid="1649848182825" $x_{2}$ denotes different levels of dummy variables used in the model

which can take value of either 0 or 1.