Answer: If independent variable X₁ increases by 1 unit, we would expect Y to increase by 0.25 units, holding X₂ constant

## 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.

Author: Nikitesh Somanthe