Consider a regression study involving a dependent variable $y$, a quantitative independent variable $x_1$, and a categorical independent variable with three possible levels (level 1, level 2, and level 3).
a. How many dummy variables are required to represent the categorical variable?
b. Write a multiple regression equation relating $x_1$ and the categorical variable to $E(y)$.
1. $E(y) = \beta_0 + \beta_1 x_1$
2. $E(y) = \beta_0 + \beta_1 x_2$
3. $E(y) = \beta_0 + \beta_1 x_3$
4. $E(y) = \beta_0 + \beta_1 x_1 + \beta_2 + \beta_3$
5. $E(y) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3$
c. Interpret the parameters in your regression equation.
Enter the values of dummy variables $x_2$ and $x_3$ that are used to indicate the three levels of the categorical variable.
Level
1
2
3
$x_2$
Select your answer
Select your answer
Select your answer
$x_3$
Select your answer
Select your answer
Select your answer
c. Interpret the parameters in your regression equation.
$\beta_0 = $ Select your answer
$\beta_1 = $ Select your answer
$\beta_2 = $ Select your answer
$\beta_3$ is the change in $E(y)$ for a 1 unit change in [Select your answer] holding the categorical variable constant.
[No new key]
Exercise 15.35 (Categorical Independent Variables)
