If the variance of u is quadratic in X, then it can be expressed as A)var(u_i|X_i)= $\theta _ { 0 } ^ { 2 }$ B)var(u_i|X_i)= ?₀+ ?₁ $x _ { i } ^ { 1 / 2 }$ C)var(u_i|X_i)= ?₀+ ?₁ $x _ { i } ^ { 2 }$ D)var(u_i|X_i)= $\sigma _ { \mathrm { u } } ^ { 2 }$

Question

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The correct choice is C because it expresses the variance of $u$ as a quadratic function of $X$, indicated by the term $x_i^2$, which aligns with the definition of variance being quadratic in $X$. Choices A and D suggest constant variances, and B suggests a variance that increases with the square root of $X$, not quadratically.

If the Variance of U Is Quadratic in X, Then θ02\theta _ { 0 } ^ { 2 }θ02​

If the Variance of U Is Quadratic in X, Then $\theta _ { 0 } ^ { 2 }$