Multiple regression analysis, econometrics, and statistics

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SUMMARY

The discussion centers on multiple regression analysis within the context of econometrics and statistics, specifically addressing the model y = B0 + B1x1 + B2x2 + u. Key points include the derivation of y hat as E[y (conditional) x1, x2] = B0 + B1x1 + B2x2, and the implications of using Ordinary Least Squares (OLS) under incorrect model assumptions. The consequences of model mis-specification lead to biased parameter estimates and invalid standard errors, particularly when omitting relevant variables or including irrelevant ones.

PREREQUISITES
  • Understanding of multiple regression models
  • Familiarity with Ordinary Least Squares (OLS) estimation
  • Knowledge of statistical concepts such as bias, variance, and homoskedasticity
  • Basic grasp of econometric theory and error terms
NEXT STEPS
  • Study the implications of model specification errors in econometrics
  • Learn about the Gauss-Markov theorem and its assumptions
  • Explore the concept of heteroskedasticity and its impact on regression analysis
  • Investigate advanced regression techniques such as Generalized Least Squares (GLS)
USEFUL FOR

Students of econometrics, statisticians, and data analysts seeking to deepen their understanding of multiple regression analysis and its practical applications in statistical modeling.

jasper90
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I am sooo lost in this class, please help.

1. Let the true (population) model be y = B0+B1x1+B2x2+u where u is an unobserved error term with u (conditional) x1, x2 and N(0, sigma^2). Hence, u is normally distributed with mean 0 and variance sigma^2 (i.e., E[u (conditional) x1, x2] = 0 and V ar(u (conditional) x1, x2) = sigma^2) conditional on the observed sample. Also, assume that Cov(x1, x2) = sigma(x1x2) does not equal 0.
a) Find y hat = E[y (conditional) x1, x2]
b) Find Var(y (conditional) x1, x2)
c) Assume that the econometrician (falsely) believes that y = B0 + B1x1 + v is the true model and
uses OLS in order to estimate this model. What are the consequences of this in terms of bias and variance
(homoskedasticity) of parameter estimates. Are the standard errors from this regression valid? If not why?
d) Assume that the econometrician (falsely) believes that y = B0 + B1x1 + B2x2 + B3x3 + v is the true
model and uses OLS in order to estimate this model. What are the consequences of this in terms of bias and
variance (homoskedasticity) of parameter estimates. Are the standard errors from this regression valid? If
not why?Please help.
 
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can anyone help? or does anyone have the link to a similar problem?
 
can someone help me out? i don't need the answer straight up, just need help even getting this started

is this right for a)?

yhat = E[y (conditional) x1, x2] = E[ B0+B1x1+B2x2+u (conditional) x1, x2] = B0+B1x1+B2x2
 
Last edited:
can someone help me with C and D? I am not rly sure what to do
 

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