Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
Assume we have the following multiple regression model: Y = b₀ + 0.25X₁ + 0.14X₂ + ε
It would be correct to say that:
Other
Community
NNikitesh
A
If the independent variable X₁ increases by 1 unit, we would expect Y to increase by 0.25 units
B
If the independent variable X₁ increases by 1 unit, we would expect Y to increase by 0.25/0.14 units
C
If independent variable X₁ increases by 1 unit, we would expect Y to increase by 0.25 units, holding X₂ constant
D
If independent variable X₂ increases by 1 unit, we would expect Y to increase by 0.25 + 0.14 units
Explanation:
Explanation
In multiple regression analysis, the interpretation of slope coefficients differs from simple linear regression. The key concept is ceteris paribus (holding other variables constant).
Why option C is correct:
- The coefficient 0.25 for X₁ represents the expected change in Y when X₁ increases by 1 unit, while holding X₂ constant
- This is known as a partial slope coefficient or partial regression coefficient
- Without the "holding X₂ constant" condition, the interpretation would be incomplete and potentially misleading
Why other options are incorrect:
- Option A: Incorrect because it omits the crucial "holding X₂ constant" condition
- Option B: Incorrect because dividing coefficients (0.25/0.14) has no meaningful interpretation in this context
- Option D: Incorrect because it adds the coefficients (0.25 + 0.14) and misattributes them to X₂
Key Concept: In multiple regression Y = β₀ + β₁X₁ + β₂X₂ + ε:
- β₁ = ∂Y/∂X₁ (partial derivative of Y with respect to X₁, holding X₂ constant)
- β₂ = ∂Y/∂X₂ (partial derivative of Y with respect to X₂, holding X₁ constant)
This ensures we isolate the effect of each independent variable while controlling for the others.
Comments
Loading comments...