Question

1) In the simple linear regression model $Y_i = \beta_0 + \beta_1 X_i + u_i$ a) Explain the difference between $\beta_1$ and the OLS estimator $\hat{\beta}_1$ b) Explain the difference between the error term $u_i$ and the OLS residual $\hat{u}_i$ c) Under the assumption that $E(u|X) = 0$ explain the difference between the population regression function $E(Y|X)$ and the OLS predicted value $\hat{Y}_i$

          1) In the simple linear regression model
$Y_i = \beta_0 + \beta_1 X_i + u_i$
a) Explain the difference between $\beta_1$ and the OLS estimator $\hat{\beta}_1$
b) Explain the difference between the error term $u_i$ and the OLS
residual $\hat{u}_i$
c) Under the assumption that $E(u|X) = 0$ explain the difference
between the population regression function $E(Y|X)$ and the OLS
predicted value $\hat{Y}_i$

1) In the simple linear regression model
Yi = β0 + β1 Xi + ui
a) Explain the difference between β1 and the OLS estimator β̂1
b) Explain the difference between the error term ui and the OLS
residual ûi
c) Under the assumption that E(u|X) = 0 explain the difference
between the population regression function E(Y|X) and the OLS
predicted value Ŷi

Added by Andrea H.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Benjamin Densmore

Step 1

It captures all the factors that affect Yi but are not included in the regression model. The error term is assumed to have a mean of zero and is independent of Xi. On the other hand, the OLS residual, denoted as u, is the difference between the observed value of Show more…

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In the simple linear regression model: Yi = Î²0 + Î²1Xi + Îµi b) Explain the difference between the error term Îµ and the OLS residual u. c) Under the assumption that E(Îµ|Xi) = 0, explain the difference between the population regression function E(Y|X) and the OLS predicted value Y.