code/Lecture5_homework2.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"AdvPythonHomework2.ipynb","provenance":[],"authorship_tag":"ABX9TyMoFJaS24YwTX0ecyj7OnO1"},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"code","metadata":{"id":"RJF3R6fa5gkk","colab_type":"code","colab":{}},"source":[""],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"-uMbqLNe5jGV","colab_type":"text"},"source":["# Homework 2\n","\n","### Building your own ANOVA reference library\n","\n","[This website](https://psychstat3.missouristate.edu/Documents/MultiBook3/Mlt08.htm) gives about 8 good examples of different types of results you can get from an ANOVA.  You can find them be scrolling to the bottom of the page.  \n","\n","**Exercise** Satisfy yourself that you agree with the interpretation given by the text for each of the 8 examples, in terms of classifying results as significant or non-significant.\n","\n","**Exercise** Determine whether the plots in these 8 examples show main effects or *simple* main effects. \n","\n","**Exercise** (Suggested in class!) The example plots on the website correspond to a 2-way ANVOA where one factor has 3 levels and one has 2.  The Italian soda example is a 2-way ANOVA with 2 levels in each factor.  Still, we can create a reasonable analog to the 2d plots from the website by rotating our 3d plots and viewing the \"cube\" from a particular side.\n","* Determine which side\n","* Which lines would we want to look at, in order to match the website plots?  The black or the magenta?\n","\n","\n","### Regression destabilizes when predictors are correlated\n","\n","Try re-running the 2-independent-variable linear regression notebook using each of the following point clouds (or just imagine that you did -- if you get to the end of this section and feel you understand everything, then you don't actually need to run the data).  Note that each of the clouds labeled \"few\" is a subsample of one of the clouds labeled \"many.\"  \n","\n","Now re-run your analysis with different subsamples of the larger clouds (or just imagine that you did -- if you get to the end of this section and agree with everything, you don't actually need to run the data).  You may find that the results you get for differen subsamples of the \"thin\" cloud change a lot more than the ones sampled from the \"wide\" cloud.  This is a general issue / phenomenon / problem in regression analysis.  **When your independent variables are strongly related to one another, your best-fit line / plane / etc can become unstable.**"]},{"cell_type":"code","metadata":{"id":"0jFHQxmQ9Tfp","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":1000},"executionInfo":{"status":"ok","timestamp":1594911511559,"user_tz":240,"elapsed":3939,"user":{"displayName":"Gregory Henselman-Petrusek","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhckxaTMcRtkWS6WTTfLWaTxbu5kyRx4KZCGhjo=s64","userId":"16161081938846221309"}},"outputId":"2a2409bd-1670-43aa-a07f-200a6ffc03eb"},"source":["import numpy as np\n","import plotly\n","import plotly.graph_objects as go\n","\n","#   SET THE NUMER OR POINTS TO GENERATE\n","sample_size     = 50\n","\n","#   SET THE NUMER OR POINTS TO SUBSAMPLE\n","subsample_size  = 8\n","\n","#   DETERMINE WHICH POINTS WE'LL SUBSAMPLE\n","subsample_set   = np.random.choice(sample_size,  subsample_size, replace=False)\n","print(f'we\\'ll subsample these rows of the matrix {subsample_set}')\n","\n","#   OUR Z-COORDINATES WILL BE RANDOM NOISE; PICK A SCALE FOR THE NOISE\n","z_scale = 0.05\n","\n","#   GENERATE TWO POINT CLOUDS\n","pcloud_widemany = np.random.rand(sample_size,3) * [1,1,2*z_scale]\n","pcloud_thinmany = np.concatenate(   (   \n","                                        np.repeat(np.random.rand(sample_size,1),2,axis=1) + np.random.rand(sample_size,2)*z_scale,\n","                                        np.random.rand(sample_size,1) * 2*z_scale\n","                                    ),\n","                                axis= 1\n","                                )\n","\n","#   SUBSAMPLE THE CLOUDS\n","pcloud_widefew = pcloud_widemany[subsample_set,:]\n","pcloud_thinfew = pcloud_thinmany[subsample_set,:]\n","\n","#   PLOT THE FOUR CLOUDS TO GET A SENSE WHAT THEY LOOK LIK\n","for pcloud in [pcloud_widemany,pcloud_widefew,pcloud_thinmany,pcloud_thinfew]:\n","  trace = go.Scatter3d(x=pcloud[:,0], y=pcloud[:,1], z=pcloud[:,2], mode='markers')\n","  scene = dict( xaxis=dict(range=[0,1]), yaxis=dict(range=[0,1]), zaxis=dict(range=[-0.5,0.5]), aspectmode = 'cube')\n","  figure = go.Figure(data=[trace],layout = go.Layout(scene=scene))\n","  figure.show()\n"],"execution_count":1,"outputs":[{"output_type":"stream","text":["we'll subsample these rows of the matrix [22 37 10  6 14 29 19  7]\n"],"name":"stdout"},{"output_type":"display_data","data":{"text/html":["<html>\n","<head><meta charset=\"utf-8\" /></head>\n","<body>\n","    <div>\n","            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>\n","                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n","        <script 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