refactored table generation and added figures
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2 changed files with 85 additions and 47 deletions
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@ -38,6 +38,11 @@
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\sectionfont{\color{report_main}}
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\subsectionfont{\color{report_third}}
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%% Add pagebreak before each section
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\let\oldsection\section
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\renewcommand\section{\clearpage\oldsection}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% This is where the actual document starts
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%
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@ -103,22 +108,31 @@ Hendrik Marcel W Tillemans\\
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% You can just write text in here as you would in any other word processor.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Question 1}
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This my answer to question 1.
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\subsection{Example}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\pagebreak
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creates a page break.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Simulation Study}
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\subsection{1.1: Generate Simulation Data}
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We investigate a linear model with noise
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\[y=\beta_0 + \beta_1 x1 + \beta_2 x2 + u\]
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where
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\[x1 \sim \mathcal{N}(3,\,6)\]
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\[x2 \sim \mathcal{N}(3,\,6)\]
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\[u \sim \mathcal{N}(0,\,3)\]
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In figure \ref{fig::plot_1_1} we have a 3D representation of the generated model.
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\begin{figure}[hb]
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\includegraphics[width=0.6\paperwidth]{../figures/question_1_1}
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\caption{Generated points for Question 1.1.}
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\label{fig::plot_1_1}
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\end{figure}
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\subsection{1.2: Linear Fit on Generated Data}
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\begin{table}[h]
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@ -159,6 +173,12 @@ creates a page break.
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\label{tab::table_1_6}
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\end{table}
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\begin{figure}[hb]
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\includegraphics[width=0.6\paperwidth]{../figures/question_1_6}
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\caption{Generated points for Question 1.6.}
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\label{fig::plot_1_6}
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\end{figure}
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\section{examples}
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Some greek letters:
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@ -65,6 +65,22 @@ np.random.seed(group_seed)
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print_line_length = 90
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print_line_start = 5
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# -----------------------------------------------------------------------------
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# Utility Functions for the Simulation
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# -----------------------------------------------------------------------------
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def results_to_latex_table_file(file_name, results, beta):
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"""
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This function takes a results object from statsmodels and writes it to a latex table file.
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"""
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d = {'True': beta,
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'Estimated': results.params,
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'Std Err': results.bse,
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't-Stat': results.tvalues}
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df = pd.DataFrame(data = d)
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data_frame_to_latex_table_file(REPORT_DIR + file_name, df)
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# -----------------------------------------------------------------------------
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# 1.1
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# -----------------------------------------------------------------------------
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@ -90,6 +106,21 @@ x2 = rng.normal(2, 5, (num_obs,))
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# y
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y = beta[0] + beta[1]*x1 + beta[2]*x2 + u
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# plot the resulting data
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fig = plt.figure()
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ax = fig.add_subplot(projection='3d')
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ax.scatter(x1, x2, y, marker='o')
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ax.set_xlabel('x1')
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ax.set_ylabel('x2')
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ax.set_zlabel('y')
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plt.savefig(FIGURE_DIR + "question_1_1.png")
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plt.show()
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# -----------------------------------------------------------------------------
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# 1.2
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# -----------------------------------------------------------------------------
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@ -101,12 +132,7 @@ X = np.array([np.ones(num_obs), x1, x2]).T
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m = sm.OLS(y, X)
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# results =
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results = m.fit()
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d = {'True': beta,
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'Estimated': results.params,
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'Std Err': results.bse,
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't-Stat': results.tvalues}
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df = pd.DataFrame(data = d)
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data_frame_to_latex_table_file(REPORT_DIR + 'table_1_2.tex', df)
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results_to_latex_table_file('table_1_2.tex', results, beta)
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# -----------------------------------------------------------------------------
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# 1.3
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@ -119,12 +145,8 @@ X = np.array([np.ones(num_obs), x1]).T
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m = sm.OLS(y, X)
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# results =
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results = m.fit()
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d = {'True': beta[0:2],
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'Estimated': results.params,
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'Std Err': results.bse,
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't-Stat': results.tvalues}
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df = pd.DataFrame(data = d)
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data_frame_to_latex_table_file(REPORT_DIR + 'table_1_3.tex', df)
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results_to_latex_table_file('table_1_3.tex', results, beta[0:2])
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# -----------------------------------------------------------------------------
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# 1.4
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@ -141,12 +163,7 @@ X = np.array([np.ones(num_obs), x1, x2_new]).T
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m = sm.OLS(y_new, X)
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# results =
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results = m.fit()
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d = {'True': beta,
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'Estimated': results.params,
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'Std Err': results.bse,
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't-Stat': results.tvalues}
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df = pd.DataFrame(data = d)
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data_frame_to_latex_table_file(REPORT_DIR + 'table_1_4.tex', df)
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results_to_latex_table_file('table_1_4.tex', results, beta)
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# -----------------------------------------------------------------------------
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# 1.5
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@ -159,30 +176,31 @@ X = np.array([np.ones(num_obs), x1]).T
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m = sm.OLS(y_new, X)
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# results =
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results = m.fit()
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d = {'True': beta[0:2],
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'Estimated': results.params,
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'Std Err': results.bse,
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't-Stat': results.tvalues}
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df = pd.DataFrame(data = d)
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data_frame_to_latex_table_file(REPORT_DIR + 'table_1_5.tex', df)
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results_to_latex_table_file('table_1_5.tex', results, beta[0:2])
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# -----------------------------------------------------------------------------
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# 1.6
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# -----------------------------------------------------------------------------
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x1 = rng.normal(3, 1, (num_obs,))
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y = beta[0] + beta[1]*x1 + beta[2]*x2 + u
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# x1 --> x1_new so we can compare to the original x1 from 1.2
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x1_new = rng.normal(3, 1, (num_obs,))
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y_new = beta[0] + beta[1]*x1_new + beta[2]*x2 + u
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# X
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X = np.array([np.ones(num_obs), x1, x2]).T
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X = np.array([np.ones(num_obs), x1_new, x2]).T
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# m
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m = sm.OLS(y, X)
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m = sm.OLS(y_new, X)
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# results =
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results = m.fit()
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d = {'True': beta,
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'Estimated': results.params,
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'Std Err': results.bse,
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't-Stat': results.tvalues}
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df = pd.DataFrame(data = d)
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data_frame_to_latex_table_file(REPORT_DIR + 'table_1_6.tex', df)
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results_to_latex_table_file('table_1_6.tex', results, beta)
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fig = plt.figure()
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ax1 = fig.add_subplot(111)
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ax1.scatter(x1, y, c='b', marker="s", label='question 1.1')
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ax1.scatter(x1_new, y_new, c='r', marker="o", label='question 1.6')
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plt.legend(loc='upper left')
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plt.savefig(FIGURE_DIR + "question_1_6.png")
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plt.show()
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