{ "metadata": { "kernelspec": { "codemirror_mode": { "name": "ipython", "version": 2 }, "display_name": "IPython (Python 2)", "language": "python", "name": "python2" }, "language": "Julia", "name": "", "signature": "sha256:3750149decaccd7a2378d026e1e9453f372e1cc1ca7503a2c5f6f6d898cba98c" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This problem is about predicting the world population. Here is a julia notebook.\n", "You can convert to any language.
\n", "Form the matrix of data for the world population from http://en.wikipedia.org/wiki/World_population, table \"Estimated world and regional populations at various dates (in millions)\" by taking the first two columns from 1950 until 2010." ] }, { "cell_type": "code", "collapsed": false, "input": [ "A=[1950 2519\n", " 1955 2756\n", " 1960 2982\n", " 1965 3335\n", " 1970 3692\n", " 1975 4068\n", " 1980 4435\n", " 1985 4831\n", " 1990 5263 \n", " 1995 5674\n", " 2000 6070\n", " 2005 6454\n", " 2010 6972];" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Column 1 of $A$ is time $t$ and column 2, population $P$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "t=A[:,1]; P=A[:,2];" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "function B(k)\n", " z=zeros(Int,13,k+1)\n", " for i=0:k z[:,i+1]=t.^i end\n", " z \n", "end" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "B (generic function with 1 method)" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now approximate the population in the least-squares sense with the \n", "function $a*\\exp(b*t)$, and with polynomials of second (quadratic), third (cubic) and fourth (quartic) degree. \n", "Plot all aproximations and the original data.\n", "Predict the current population by each approximation and compare to the current population from \n", "http://www.worldometers.info/world-population/ (Looks like 7266 so far this year on October 10, 2014 )
\n", "\n", "Suppose we say 7266 + 63*(80/365) is the actual number this year -- you might be able to be a bit more accurate." ] }, { "cell_type": "code", "collapsed": false, "input": [ "actual = 7266 + 63*(80/365) " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 40, "text": [ "7279.808219178082" ] } ], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "B(2) # Quadratic" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "13x3 Array{Int64,2}:\n", " 1 1950 3802500\n", " 1 1955 3822025\n", " 1 1960 3841600\n", " 1 1965 3861225\n", " 1 1970 3880900\n", " 1 1975 3900625\n", " 1 1980 3920400\n", " 1 1985 3940225\n", " 1 1990 3960100\n", " 1 1995 3980025\n", " 1 2000 4000000\n", " 1 2005 4020025\n", " 1 2010 4040100" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "c=B(2)\\P" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "3-element Array{Float64,1}:\n", " -0.0714 \n", " -70.6796 \n", " 0.0368522" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evaluate the polynomial and plot it" ] }, { "cell_type": "code", "collapsed": false, "input": [ "z(k)=[B(k) ;2014.^(0:k)']" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "z (generic function with 1 method)" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "z(2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "14x3 Array{Int64,2}:\n", " 1 1950 3802500\n", " 1 1955 3822025\n", " 1 1960 3841600\n", " 1 1965 3861225\n", " 1 1970 3880900\n", " 1 1975 3900625\n", " 1 1980 3920400\n", " 1 1985 3940225\n", " 1 1990 3960100\n", " 1 1995 3980025\n", " 1 2000 4000000\n", " 1 2005 4020025\n", " 1 2010 4040100\n", " 1 2014 4056196" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": true, "input": [ "using PyPlot" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "INFO: Loading help data...\n" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(t,P,\"*\")\n", "plot([t;2014],z(2)*c)\n", "plot(2014,7266,\"r*\")\n", "xlabel(\"year\")\n", "ylabel(\"Population in millions\")\n", "title(\"World Population Growth using a quadratic fit\")\n", "legend({\"Actual\",\"Predicted\"},loc=\"upper left\")\n", "savefig(\"PopulationGrowth\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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", "text": [ "Figure(PyObject )" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "nmax=4\n", "plot(t,P,\"*\")\n", "for n=2:nmax\n", " c=B(n)\\P\n", " plot([t;2014],z(n)*c)\n", " println(\"degree $(n): 2014 Estimate: $(round(z(n)*c)[end]) Actual: $(round(actual))\")\n", "end \n", "plot(2014,actual,\"r*\")\n", "xlabel(\"year\")\n", "ylabel(\"Population in millions\")\n", "title(\"World Population Growth\")\n", "legend({\"Actual\", (2:nmax)...},loc=\"upper left\")\n", "#savefig(\"PopulationGrowth\")" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "degree 2: 2014 Estimate: 7131.0 Actual: 7280.0\n", "degree 3: 2014 Estimate: 7160.0 Actual: 7280.0\n", "degree 4: 2014 Estimate: 7188.0 Actual: 7280.0\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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", "text": [ "Figure(PyObject )" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 43, "text": [ "PyObject " ] } ], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do polynomials keep getting better? Or eventually do they breakdown? Submit graphs and writeup as evidence.\n", "In juliabox you can run savefig(\"PopulationGrowth\") and then you can see the file by going file-->open\n", "in ijulia or by clicking on the home page. The browser print button will let you print" ] }, { "cell_type": "code", "collapsed": false, "input": [ "We were hoping for better luck with an exponential fit. It was not a good fit.\n", "Nonetheless explain how this works:" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "c=[t.^0 t]\\log(P)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 44, "text": [ "2-element Array{Float64,1}:\n", " -25.7489 \n", " 0.017232" ] } ], "prompt_number": 44 }, { "cell_type": "code", "collapsed": false, "input": [ "exp(c[1] + 2014 * c[2] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 45, "text": [ "7756.98309596893" ] } ], "prompt_number": 45 } ], "metadata": {} } ] }