From 7351fd41ccec3d7b73ca3ef14324d5e7a3ea6e8d Mon Sep 17 00:00:00 2001
From: Hendrik Tillemans <hendrik@snamellit.com>
Date: Mon, 30 Dec 2024 16:13:24 +0100
Subject: [PATCH] added content

---
 report/Assignment.tex | 28 ++++++++++++++++++----------
 1 file changed, 18 insertions(+), 10 deletions(-)

diff --git a/report/Assignment.tex b/report/Assignment.tex
index d14f1c4..c99d498 100644
--- a/report/Assignment.tex
+++ b/report/Assignment.tex
@@ -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}