world:quiz2
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world:quiz2 [2025/10/01 00:57] rdouc created |
world:quiz2 [2025/10/01 22:14] (current) rdouc |
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| $\begin{pmatrix}{\tilde \beta}_1\\ {\tilde \beta}_2 \end{pmatrix}=(X'X)^{-1}X'Y$. | $\begin{pmatrix}{\tilde \beta}_1\\ {\tilde \beta}_2 \end{pmatrix}=(X'X)^{-1}X'Y$. | ||
| Which of the following statements are always true: | Which of the following statements are always true: | ||
| - | - $\tilde \beta_1$ is an unbiased estimator of $\beta_1$. | + | - $\tilde \beta_1$ is an unbiased estimator of $\beta_1$. VRAI |
| - | - $\PE[\tilde \beta_2]=0$. | + | - $\PE[\tilde \beta_2]=0$. VRAI |
| - | - Using the Gauss-Markov theorem, we can show that $V (\hat \beta_1) \leq V(\tilde \beta_1)$. | + | - Using the Gauss-Markov theorem, we can show that $V (\hat \beta_1) \leq V(\tilde \beta_1)$. VRAI |
| - | - $\mathrm{Var}(\hat \beta_1)= \frac{\sigma^2}{\sum_{i=1}^n x_{i,1}^2/n - (\sum_{i=1}^n x_{i,1}/n)^2 }$. | + | - $\mathrm{Var}(\hat \beta_1)= \frac{\sigma^2}{\sum_{i=1}^n x_{i,1}^2/n - (\sum_{i=1}^n x_{i,1}/n)^2 }$. FAUX |
| - | - $\mathrm{Var}(\hat \beta_1)= \frac{\sigma^2}{\sum_{i=1}^n x_{i,1}^2}$. | + | - $\mathrm{Var}(\hat \beta_1)= \frac{\sigma^2}{\sum_{i=1}^n x_{i,1}^2}$. VRAI |
| - | - $\mathrm{Var}(\hat \beta_1)= \frac{\sigma^2}{\sum_{i=1}^n x_{i,1}^2/n}$. | + | - $\mathrm{Var}(\hat \beta_1)= \frac{\sigma^2}{\sum_{i=1}^n x_{i,1}^2/n}$. FAUX |
world/quiz2.1759273078.txt.gz · Last modified: 2025/10/01 00:57 by rdouc
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