Question

Split the data into two: one for smokers and the other for nonsmokers. Fit the model below for smoking children:
FEV1_i = β₀ + β₁ (AGE_i-10) + ε_i
Fit the model below for nonsmoking children:
FEV1_i = γ₀ + γ₁ (AGE_i-10) + ε_i
If β₁= γ₁, then there is no interaction between AGE and SMOKE. What is the advantage of fitting one model (shown below with the interaction term) as opposed to fitting two separate models, one for each smoking status?
FEV1_i = δ₀ + δ₁ SMOKE_i + δ₂ (AGE_i-10) + δ₃ SMOKE_i(AGE_i - 10) + ε_i

Group of answer choices

A. The intercept will have a meaningful interpretation.

B. The slope will have a meaningful interpretation.

C. The p-value for the difference (β₁ - γ₁) can be calculated.

D. All of the above

Answer 1

The answer is:

D. All of the above

The combined model is:

FEV1_i = δ₀ + δ₁ SMOKE_i + δ₂ (AGE_i-10) + δ₃ SMOKE_i(AGE_i - 10) + ε_i

Adding an interaction term in the model expands our understanding of the relationships among the variables and drastically changes the interpretations of the coefficients used in the particular model. Both the slope and intercept will have meaningful interpretations. The p-value for the difference (β₁ - γ₁) can be calculated as well through the analysis of the interaction term.

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!