report/Assignment.tex

@@ -38,11 +38,6 @@
 \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
 % 
@@ -108,31 +103,22 @@ 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{1.1: Generate Simulation Data}
-
-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]
@@ -173,12 +159,6 @@ In figure \ref{fig::plot_1_1} we have a 3D representation of the generated model
 \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

@@ -1,14 +0,0 @@
-\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

@@ -65,22 +65,6 @@ 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
 # -----------------------------------------------------------------------------
@@ -106,21 +90,6 @@ 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
 # -----------------------------------------------------------------------------
@@ -132,7 +101,12 @@ X = np.array([np.ones(num_obs), x1, x2]).T
 m = sm.OLS(y, X)
 # results = 
 results = m.fit()
-results_to_latex_table_file('table_1_2.tex', results, beta)
+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 + 'table_1_2.tex', df)
 
 # -----------------------------------------------------------------------------
 # 1.3
@@ -145,8 +119,12 @@ X = np.array([np.ones(num_obs), x1]).T
 m = sm.OLS(y, X)
 # results = 
 results = m.fit()
-results_to_latex_table_file('table_1_3.tex', results, beta[0:2])
-
+d = {'True': 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
@@ -163,7 +141,12 @@ X = np.array([np.ones(num_obs), x1, x2_new]).T
 m = sm.OLS(y_new, X)
 # results = 
 results = m.fit()
-results_to_latex_table_file('table_1_4.tex', results, beta)
+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 + 'table_1_4.tex', df)
 
 # -----------------------------------------------------------------------------
 # 1.5
@@ -176,31 +159,30 @@ X = np.array([np.ones(num_obs), x1]).T
 m = sm.OLS(y_new, X)
 # results = 
 results = m.fit()
-results_to_latex_table_file('table_1_5.tex', results, beta[0:2])
+d = {'True': 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 --> x1_new so we can compare to the original x1 from 1.2
-x1_new = rng.normal(3, 1, (num_obs,))
-y_new = beta[0] + beta[1]*x1_new + beta[2]*x2 + u
+x1 = rng.normal(3, 1, (num_obs,))
+y = beta[0] + beta[1]*x1 + beta[2]*x2 + u
 
 # X 
-X = np.array([np.ones(num_obs), x1_new, x2]).T
+X = np.array([np.ones(num_obs), x1, x2]).T
 
 # m
-m = sm.OLS(y_new, X)
+m = sm.OLS(y, X)
 # results = 
 results = m.fit()
-results_to_latex_table_file('table_1_6.tex', results, beta)
-
-fig = plt.figure()
-ax1 = fig.add_subplot(111)
-
-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()
-
+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 + 'table_1_6.tex', df)