You are interested in determining the factors that determine the wealth of a person and assume that the age of a person may have a non-linear effect on wealth.You run the following regression: Y = β₀ + β₁X₁ + β₂X₂ + β₃

+ β₄X₃ + ε where Y is the total wealth and X₂is the person's age.What would be your H₀regarding β₂ and β₃?

Question

You are interested in determining the factors that determine the wealth of a person and assume that the age of a person may have a non-linear effect on wealth.You run the following regression: Y = β₀ + β₁X₁ + β₂X₂ + β₃

+ β₄X₃ + ε where Y is the total wealth and X₂is the person's age.What would be your H₀regarding β₂ and β₃?

Quizplus · Accepted Answer

The regression equation includes two coefficients for the age variable, β₂ and β₃, which suggest a non-linear effect of age on wealth. In particular, β₂ represents the effect of age on wealth when age is positive, while β₃ captures the effect of age on wealth when age is negative. Since the question assumes that age has a non-linear effect on wealth, we can expect that the two coefficients will have opposite signs. Specifically, β₂ should be positive (indicating that wealth increases with age for some range of ages) while β₃ should be negative (indicating that wealth decreases with age for some range of ages). Therefore, the best choice is C, which states that β₂ > 0 and β₃ < 0.

You Are Interested in Determining the Factors That Determine the Wealth