~N(0₂exp(x) 5. Consider the following data generating process (DGP): y = a + ßx+u, where x ~ N(2,2²¹), u ~] and ß = 2. ( a) Consider a weighted least squared (WLS) regression: < y α u 1 √h(x) √h(x) √h(x) ' exp(x) Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not.< = + √h(x) B+ where h(x)= = H b) Consider another weighted least squared (WLS) regression but with a misspecified h(x): < y α x √h(x)=√h(x) + √h(x) B+ where h(x) = x².< u √h(x) ' Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not. < a=1, c) Use Stata to generate a random sample of n = 1,000 from the DGP. Set "seed" to be your student number so you can replicate the same results. Estimate the WLS regressions in (b) and (c). In real-world applications, do we know h(x)?<

Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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5. Consider the following data generating process (DGP): y = a + fx + u, where x ~ N(2,2²¹), u ~ N(0₂ex(x)), a=1,
and ß = 2. <
a) Consider a weighted least squared (WLS) regression: <
y
α
X
U
1
√(x)=√(x) + √(x) B+ √(x), where h(x) exp(x)
Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not.<
=
=
b) Consider another weighted least squared (WLS) regression but with a misspecified h(x):
α
X
น
+ B + where h(x)=x².<
√h(x) √h(x) √h(x) √h(x)
9
Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not. <
[h(x)
c) Use Stata to generate a random sample of n = 1,000 from the DGP. Set "seed" to be your student number so
you can replicate the same results. Estimate the WLS regressions in (b) and (c). In real-world applications,
do we know h(x)?↔
Transcribed Image Text:1 5. Consider the following data generating process (DGP): y = a + fx + u, where x ~ N(2,2²¹), u ~ N(0₂ex(x)), a=1, and ß = 2. < a) Consider a weighted least squared (WLS) regression: < y α X U 1 √(x)=√(x) + √(x) B+ √(x), where h(x) exp(x) Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not.< = = b) Consider another weighted least squared (WLS) regression but with a misspecified h(x): α X น + B + where h(x)=x².< √h(x) √h(x) √h(x) √h(x) 9 Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not. < [h(x) c) Use Stata to generate a random sample of n = 1,000 from the DGP. Set "seed" to be your student number so you can replicate the same results. Estimate the WLS regressions in (b) and (c). In real-world applications, do we know h(x)?↔
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