Researchers are interested in how mean medical expenditures is associated with i

Question

Researchers are interested in how mean medical expenditures is associated with income. They use a multiple linear regression model to predict medical expenditures using income and age. They include an interaction between income and age in the model. The interaction term is statistically significant, but the main effect (coefficient) of age is not statistically significant. Therefore o The association between age and medical expenditures does not vary by income o The association between age and medical expenditures when income is 0 is not statistically significant. o The association between age and medical expenditures varies by income, but the the association between income and medical expenditures does not vary by age O The association between age and medical expenditures is not statistically significant, controlling for income.

Explanation / Answer

Ans:

Second option is correct.

The association between age and medical expenditures when income is 0 is not statistically significant.

For example:

If the interaction is significant, interpreting either main effect, whether significant or not, is basically pointless (and misleading). The reason is that when A and B are involved in an interaction, the coefficient for A is the effect of A when B=0; in other words, the effect is conditional on the value of B, and is not a main effect. Similarly, the coefficient for B is the effect of B when A=0.

The fact that A is significant merely means that A has an effect when B=0. Similarly, the fact that B is not significant merely means that B doesn't have an effect when A=0, though it probably does have an effect for other values of A; this is precisely why the interaction is significant.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.