Slopes and Lines.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MSDS 400 Slopes and Lines\n",
    "\n",
    "\n",
    "The results will appear below or in a separate window which will reveal the plots.  Print statements will be used to separate sections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot \n",
    "from matplotlib.pyplot import *\n",
    "import numpy \n",
    "from numpy import linspace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Equation Construction\n",
    "Find the equation of the line L passing through the point (3, 7) and perpendicular to the line 5x - y = 4.\n",
    "\n",
    "Note: The use of \\n causes a line to be skipped before the text is printed.  The characters \\n are otherwise ignored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1= 5.0\n",
    "y1= 4.0\n",
    "x2= -10.0\n",
    "y2= -2.0\n",
    "slope= (y2-y1)/(x2-x1)\n",
    "slope"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next example will show how to use the calculated slope to form the linear equation and calculate a result.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Value of y if x is 1.0 equals 2.4\n"
     ]
    }
   ],
   "source": [
    "x= 1.0\n",
    "y= y1 + slope*(x-x1)\n",
    "print('\\nValue of y if x is 1.0 equals {}'.format(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next section shows how to assign a string to a variable for printing purposes.  The variable is called \"equation\" and it will be printed as a string.  This is a useful technique that will be used in later modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation of a line is y = y1 + slope*(x-x1)\n",
      "x1 equals 5.0 and y1 equas 4.0\n"
     ]
    }
   ],
   "source": [
    "equation= str('y = y1 + slope*(x-x1)')\n",
    "print('Equation of a line is', equation)\n",
    "print('x1 equals {} and y1 equas {}'.format(x1, y1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next example will show how to plot the line y = -1.5x + 6. Plotting limits need to be set to define the dimensions of the plot.  The  linspace statement divides the interval [-1,8] into 100 points including the first, -1, and the last 100. If you have doubts about the contents or the  length of x, enter either the statements print x or len(x) in the interpreter to see the contents or find out the length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x= linspace(-1,8,100)\n",
    "y= 6.0 - 1.5*x  \n",
    "title('Plot of Linear Equation  '+equation)  # Note how the title appears.\n",
    "plot(x,y)\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next example will show how to determine the break-even point graphically using Python.  Note that integers and floating point numbers can combined in the same equation.  The result is a floating point number.  The figure() statement separates the following plot from the previous plot. Two windows will appear with separate plots one behind the other."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A firm producing poultry feed finds that the total cost C(x) in dollars of producing sand selling x units is given by C(x) = 20x + 100. Management plans to charge $24 per unit for the feed. How many units must be sold for the firm to break even?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x= linspace(0,50,100)\n",
    "y= 20*x+100.0\n",
    "z= 24*x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "loc=2 places the legend in he upper left corner.  The order in which these statements appear is important.  legend() will associate 'cost' with the first statement and 'revenue' with the second. For more information about plot(), type the phrase  plot?  in the interpreter and enter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()  \n",
    "plot (x,y)\n",
    "plot (x,z)\n",
    "legend (('cost','revenue'),loc=2)\n",
    "title ('Breakeven Analysis')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least Squares Lines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the least squares line and correlation coefficient for the accidental date rate data in the table below. Let x represent the years since 1900.\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th>Year</th>\n",
    "        <th>Death Rate</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>1920</td>\n",
    "        <td>71.2</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>1930</td>\n",
    "        <td>80.5</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>1940</td>\n",
    "        <td>73.4</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>1950</td>\n",
    "        <td>60.3</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>1960</td>\n",
    "        <td>52.1</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>1970</td>\n",
    "        <td>56.2</td>\n",
    "    <tr>\n",
    "        <td>1980</td>\n",
    "        <td>46.5</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>1990</td>\n",
    "        <td>36.9</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>2000</td>\n",
    "        <td>34.0</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>2010</td>\n",
    "        <td>39.1</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope =  -0.506\n",
      "intercept =  87.9\n",
      "The death rate in 2020 will be approximately 27.2 per 100,000 population.\n",
      "correlation coefficient =  -0.941\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "x = [20, 30, 40, 50, 60, 70, 80, 90, 100, 110]\n",
    "y = [71.2, 80.5, 73.4, 60.3, 52.1, 56.2, 46.5, 36.9, 34.0, 39.1]\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)\n",
    "predict_2020 = 120 * slope + intercept\n",
    "print(\"slope = \", round(slope, 3))\n",
    "print(\"intercept = \", round(intercept, 1))\n",
    "print(\"The death rate in 2020 will be approximately\", round(predict_2020, 1), \"per 100,000 population.\")\n",
    "print(\"correlation coefficient = \", round(r_value, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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