fixed conflict

report/Assignment.tex

@@ -38,6 +38,11 @@
 \sectionfont{\color{report_main}}
 \subsectionfont{\color{report_third}}
 
+%% Add pagebreak before each section
+\let\oldsection\section
+\renewcommand\section{\clearpage\oldsection}
+
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % This is where the actual document starts
 % 
@@ -103,26 +108,36 @@ Hendrik Marcel W Tillemans\\
 % You can just write text in here as you would in any other word processor.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\section{Question 1}
-
-This my answer to question 1.
-
-\subsection{Example}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\pagebreak
-
-creates a page break.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
 
 \section{Simulation Study}
 
+
 \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
+
+\[y=\beta_0 + \beta_1 x1 + \beta_2 x2 + u\]
+
+where
+
+\[x1 \sim \mathcal{N}(3,\,6)\]
+\[x2 \sim \mathcal{N}(3,\,6)\]
+\[u \sim \mathcal{N}(0,\,3)\]
+
+In figure \ref{fig::plot_1_1} we have a 3D representation of the generated model.
+
+\begin{figure}[hb]
+\includegraphics[width=0.6\paperwidth]{../figures/question_1_1}
+\caption{Generated points for Question 1.1.}
+\label{fig::plot_1_1}
+\end{figure}
+
+
+
+\subsection{1.2: Linear Fit on Generated Data}
+
 \begin{table}[h]
 \input{table_1_2}
 \caption{Linear Fit on Generated Data}
@@ -167,6 +182,12 @@ Linear Regression mode.
 \label{tab::table_1_6}
 \end{table}
 
+\begin{figure}[hb]
+\includegraphics[width=0.6\paperwidth]{../figures/question_1_6}
+\caption{Generated points for Question 1.6.}
+\label{fig::plot_1_6}
+\end{figure}
+
 \section{examples}
 Some greek letters:
 

report/sample_table.tex

@@ -0,0 +1,14 @@
+\begin{tabular}{lrrrr}
+\toprule
+ & Petal Width & Petal Length & Sepal Width & Sepal Length \\
+\midrule
+count & 150.000000 & 150.000000 & 150.000000 & 150.000000 \\
+mean & 5.843333 & 3.057333 & 3.758000 & 1.199333 \\
+std & 0.828066 & 0.435866 & 1.765298 & 0.762238 \\
+min & 4.300000 & 2.000000 & 1.000000 & 0.100000 \\
+25% & 5.100000 & 2.800000 & 1.600000 & 0.300000 \\
+50% & 5.800000 & 3.000000 & 4.350000 & 1.300000 \\
+75% & 6.400000 & 3.300000 & 5.100000 & 1.800000 \\
+max & 7.900000 & 4.400000 & 6.900000 & 2.500000 \\
+\bottomrule
+\end{tabular}

scripts/simulation.py

@@ -65,6 +65,22 @@ np.random.seed(group_seed)
 print_line_length = 90
 print_line_start = 5
 
+
+# -----------------------------------------------------------------------------
+# Utility Functions for the Simulation
+# -----------------------------------------------------------------------------
+
+def results_to_latex_table_file(file_name, results, beta):
+    """
+    This function takes a results object from statsmodels and writes it to a latex table file.
+    """
+    d = {'True': beta, 
+         'Estimated': results.params, 
+         'Std Err': results.bse, 
+         't-Stat': results.tvalues}
+    df = pd.DataFrame(data = d)
+    data_frame_to_latex_table_file(REPORT_DIR + file_name, df)
+
 # -----------------------------------------------------------------------------
 # 1.1
 # -----------------------------------------------------------------------------
@@ -90,6 +106,21 @@ x2 = rng.normal(2, 5, (num_obs,))
 # y 
 y = beta[0] + beta[1]*x1 + beta[2]*x2 + u
 
+
+# plot the resulting data
+fig = plt.figure()
+ax = fig.add_subplot(projection='3d')
+
+ax.scatter(x1, x2, y, marker='o')
+
+ax.set_xlabel('x1')
+ax.set_ylabel('x2')
+ax.set_zlabel('y')
+
+plt.savefig(FIGURE_DIR + "question_1_1.png")
+plt.show()
+
+
 # -----------------------------------------------------------------------------
 # 1.2
 # -----------------------------------------------------------------------------
@@ -101,12 +132,7 @@ X = np.array([np.ones(num_obs), x1, x2]).T
 m = sm.OLS(y, X)
 # results = 
 results = m.fit()
-d = {'True': beta, 
+results_to_latex_table_file('table_1_2.tex', results, beta)
-     'Estimated': results.params, 
-     'Std Err': results.bse, 
-     't-Stat': results.tvalues}
-df = pd.DataFrame(data = d)
-data_frame_to_latex_table_file(REPORT_DIR + 'table_1_2.tex', df)
 
 # -----------------------------------------------------------------------------
 # 1.3
@@ -119,12 +145,8 @@ X = np.array([np.ones(num_obs), x1]).T
 m = sm.OLS(y, X)
 # results = 
 results = m.fit()
-d = {'True': beta[0:2], 
+results_to_latex_table_file('table_1_3.tex', results, beta[0:2])
-     'Estimated': results.params, 
+
-     'Std Err': results.bse, 
-     't-Stat': results.tvalues}
-df = pd.DataFrame(data = d)
-data_frame_to_latex_table_file(REPORT_DIR + 'table_1_3.tex', df)
 
 # -----------------------------------------------------------------------------
 # 1.4
@@ -141,12 +163,7 @@ X = np.array([np.ones(num_obs), x1, x2_new]).T
 m = sm.OLS(y_new, X)
 # results = 
 results = m.fit()
-d = {'True': beta, 
+results_to_latex_table_file('table_1_4.tex', results, beta)
-     'Estimated': results.params, 
-     'Std Err': results.bse, 
-     't-Stat': results.tvalues}
-df = pd.DataFrame(data = d)
-data_frame_to_latex_table_file(REPORT_DIR + 'table_1_4.tex', df)
 
 # -----------------------------------------------------------------------------
 # 1.5
@@ -159,30 +176,31 @@ X = np.array([np.ones(num_obs), x1]).T
 m = sm.OLS(y_new, X)
 # results = 
 results = m.fit()
-d = {'True': beta[0:2], 
+results_to_latex_table_file('table_1_5.tex', results, beta[0:2])
-     'Estimated': results.params, 
-     'Std Err': results.bse, 
-     't-Stat': results.tvalues}
-df = pd.DataFrame(data = d)
-data_frame_to_latex_table_file(REPORT_DIR + 'table_1_5.tex', df)
 
 # -----------------------------------------------------------------------------
 # 1.6
 # -----------------------------------------------------------------------------
 
-x1 = rng.normal(3, 1, (num_obs,))
+# x1 --> x1_new so we can compare to the original x1 from 1.2
-y = beta[0] + beta[1]*x1 + beta[2]*x2 + u
+x1_new = rng.normal(3, 1, (num_obs,))
+y_new = beta[0] + beta[1]*x1_new + beta[2]*x2 + u
 
 # X 
-X = np.array([np.ones(num_obs), x1, x2]).T
+X = np.array([np.ones(num_obs), x1_new, x2]).T
 
 # m
-m = sm.OLS(y, X)
+m = sm.OLS(y_new, X)
 # results = 
 results = m.fit()
-d = {'True': beta, 
+results_to_latex_table_file('table_1_6.tex', results, beta)
-     'Estimated': results.params, 
+
-     'Std Err': results.bse, 
+fig = plt.figure()
-     't-Stat': results.tvalues}
+ax1 = fig.add_subplot(111)
-df = pd.DataFrame(data = d)
+
-data_frame_to_latex_table_file(REPORT_DIR + 'table_1_6.tex', df)
+ax1.scatter(x1, y, c='b', marker="s", label='question 1.1')
+ax1.scatter(x1_new, y_new, c='r', marker="o", label='question 1.6')
+plt.legend(loc='upper left')
+plt.savefig(FIGURE_DIR + "question_1_6.png")
+plt.show()
+