Suppose you are forecasting business cycles, which relate Y; (real GDP) to time (Xi), and you...

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Suppose you are forecasting business cycles, which relate Y; (real GDP) to time (Xi), and you believe the (true) CEF is something like m(x) = 3 sin(x). (a) (5 points) What is the Taylor series approximation of m(x) to degree 4 about the point X₁ = 0? What is largest magnitude of error in this approximation? (b) (5 points) What linear regression equation can measure the approximation from (a)? What are the values of the coefficients in this equation? What is the residual (€;)? (c) (5 points) If you consider E[e;|X; = x], is this zero? Why or why not? Suppose you are forecasting business cycles, which relate Y; (real GDP) to time (Xi), and you believe the (true) CEF is something like m(x) = 3 sin(x). (a) (5 points) What is the Taylor series approximation of m(x) to degree 4 about the point X₁ = 0? What is largest magnitude of error in this approximation? (b) (5 points) What linear regression equation can measure the approximation from (a)? What are the values of the coefficients in this equation? What is the residual (€;)? (c) (5 points) If you consider E[e;|X; = x], is this zero? Why or why not?