Consider a regression study involving a dependent variable y, a quantitative independent variable 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 ₁ and the categorical variable to y. 1. E(g) = Ba + Biển 2. E(y) = Bo + By 3. E(y) = 0 + B3X3 4. E(y)= Bo + B₁21 + B₂ + B3 5. E(y) Bo + B₁x1 + B₂x₂ + 3x3 - Select your answer v Enter the values of dummy variables 2 and 3 that are used to indicate the three levels of the categorical variable. Level 1 2 3 1 0 0 X2 W Y 0 V 0 1 X3 c. Interpret the parameters in your regression equation. Y V
Consider a regression study involving a dependent variable y, a quantitative independent variable 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 ₁ and the categorical variable to y. 1. E(g) = Ba + Biển 2. E(y) = Bo + By 3. E(y) = 0 + B3X3 4. E(y)= Bo + B₁21 + B₂ + B3 5. E(y) Bo + B₁x1 + B₂x₂ + 3x3 - Select your answer v Enter the values of dummy variables 2 and 3 that are used to indicate the three levels of the categorical variable. Level 1 2 3 1 0 0 X2 W Y 0 V 0 1 X3 c. Interpret the parameters in your regression equation. Y V
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
Transcribed Image Text:Consider a regression study involving a dependent variable y, a quantitative independent variable 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 ₁ and the categorical variable to y.
1. E(y) Bo + B₁x1
2. E(y) = Bo + B
3. E(y) Bo + B3X3
4. E(y) Bo + B₁x1 + B₂+ B3
5. E(y) = Bo + B₁x1 + B₂x₂ + B3X3
Select your answer - V
Enter the values of dummy variables 2 and 3 that are used to indicate the three levels of the categorical variable.
Level
1
2
=
3
1
0
0
X2
V
V
0
0
1
X3
c. Interpret the parameters in your regression equation.
B₂= E(yllevel 2) - E(y|level1) ✓
B3 = E(y level3) - E(y|level2) ✓
B₁ is the change in E(y) for a 1 unit change in [x2
✓ holding the categorical variable constant.
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