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Hendrik Tillemans 2024-12-30 16:13:24 +01:00
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report/Assignment.tex
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@ -119,15 +119,18 @@ creates a page break.
\section{Simulation Study}
\subsection{1.2: Linear Fit on Generated Data}
\subsection{Question 1.2}
Are the estimates of $\beta_0$, $\beta_1$ and $\beta_2$ close to their true values? Why (not)?
\begin{table}[h]
\input{table_1_2}
\caption{Linear Fit on Generated Data}
\label{tab::table_1_2}
\end{table}
\subsection{1.3: Linear Fit with 1 Variable}
\subsection{Question 1.3}
Compare your estimates with those of question 1.2. Wich model do you choose? Discuss in terms of $\beta_1$ and model prediction.
\begin{table}[h]
\input{table_1_3}
@ -135,24 +138,29 @@ creates a page break.
\label{tab::table_1_3}
\end{table}
\subsection{1.4: New Linear Fit on Generated Data}
\subsection{Question 1.4}
Do the results confirm what you would have expected to change in your estimation results compared to the results in question 1.2? Why (not)? How about the standard errors of the estimates of $\beta_1$ and $\beta_2$?
\begin{table}[h]
\input{table_1_4}
\caption{New Linear Fit on Generated Data}
\label{tab::table_1_4}
\end{table}
\subsection{1.5: New Linear Fit with 1 Variable}
\subsection{Question 1.5}
Are the OLS estimators for the slope coefficients biased? Why (not)?
\begin{table}[h]
\input{table_1_5}
\caption{Linear Fit with 1 Variable}
\label{tab::table_1_5}
\end{table}
\subsection{1.6: Generate Data with Small Variance on x1}
\subsection{Question 1.6}
Do the results confirm what you would have
expected to change in your estimation results compared to the results in question 1.2?
Why (not)? How about the standard errors of the estimates of $\beta_1$ ? Use the formula
Var$\beta_1$ to motivate your answer. What would happen if the standard deviation of x1
is equal to 0 instead of equals 1? Discuss in terms of the assumptions of the Multiple
Linear Regression mode.
\begin{table}[h]
\input{table_1_6}
\caption{Generate Data with Small Variance on x1}