Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + ε, where the dummy variables Spring, Summer, and Fall represent the qualitative variable Season (spring, summer, fall, winter) , and the dummy variable Rain is defined as Rain = 1 if rainy day, Rain = 0 otherwise.
Assuming the same temperature and precipitation condition, what is the difference between the predicted humidity for summer and fall days?

Question

Quizplus · Accepted Answer

To find the difference between the predicted humidity for summer and fall days, we need to find the difference in the coefficients for the dummy variables representing summer and fall, that is β₃ and β₄. The coefficient for the intercept (β) and the temperature variable (β₁) are assumed to be the same for both summer and fall days since the question specifies the same temperature and precipitation condition. Thus, we can factor out their common values from the equation. The equation becomes: Humidity = (β₀) + (β₂)Spring + (β₃)Summer + (β₄)Fall + (β₅)Rain + ε We can now compare the predicted humidity for summer and fall days by subtracting β₄ from β₃: β₃ - β₄ = _b₃ - b₄

Consider the Following Regression Model: Humidity = β0 + β1Temperature

Consider the Following Regression Model: Humidity = β₀ + β₁Temperature