fixed conflict

report/Assignment.tex

@@ -111,8 +111,11 @@ Hendrik Marcel W Tillemans\\
 
 \section{Simulation Study}
 
-\subsection{1.1: Generate Simulation Data}
 
+\subsection{Question 1.2}
+ Are the estimates of $\beta_0$, $\beta_1$ and $\beta_2$ close to their true values? Why (not)?
+ 
+ 
 We investigate a linear model with noise
 
 \[y=\beta_0 + \beta_1 x1 + \beta_2 x2 + u\]
@@ -140,8 +143,9 @@ In figure \ref{fig::plot_1_1} we have a 3D representation of the generated model
 \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}
@@ -149,24 +153,29 @@ In figure \ref{fig::plot_1_1} we have a 3D representation of the generated model
 \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}