Changed covariance explantion

`

05-Multivariate-Gaussians.ipynb

@@ -234,7 +234,7 @@
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        "                        TeX: {\n",
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+       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
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@@ -299,9 +299,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In the last two chapters we used Gaussians for a scalar (one dimensional) variable, expressed as $\\mathcal{N}(\\mu, \\sigma^2)$. A more formal term for this is **univariate normal**, where univariate means 'one variable'. The probability distribution of the Gaussian is known as the **univariate normal distribution**\n",
+    "In the last two chapters we used Gaussians for a scalar (one dimensional) variable, expressed as $\\mathcal{N}(\\mu, \\sigma^2)$. A more formal term for this is *univariate normal*, where univariate means 'one variable'. The probability distribution of the Gaussian is known as the *univariate normal distribution*.\n",
     "\n",
-    "What might a **multivariate normal distribution** be? *Multivariate* means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. I don't necessarily mean spatial dimensions - it could be position, velocity, and acceleration. Consider a two dimensional case. Let's say we believe that $x = 2$ and $y = 17$. This might be the *x* and *y* coordinates for the position of our dog, it might be the  position and velocity of our dog on the x-axis, or the temperature and wind speed at our weather station. It doesn't really matter. We can see that for $N$ dimensions, we need $N$ means, which we will arrange in a column matrix (vector) like so:\n",
+    "What might a *multivariate normal distribution* be? *Multivariate* means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. I don't necessarily mean spatial dimensions - it could be position, velocity, and acceleration. Consider a two dimensional case. Let's say we believe that $x = 2$ and $y = 17$. This might be the *x* and *y* coordinates for the position of our dog, it might be the  position and velocity of our dog on the x-axis, or the temperature and wind speed at our weather station. It doesn't really matter. We can see that for $N$ dimensions, we need $N$ means, which we will arrange in a column matrix (vector) like so:\n",
     "\n",
     "$$\n",
     "\\mu = \\begin{bmatrix}\\mu_1\\\\\\mu_2\\\\ \\vdots \\\\\\mu_n\\end{bmatrix}\n",
@@ -317,15 +317,53 @@
     "\n",
     "$$\\sigma^2 = \\begin{bmatrix}10\\\\4\\end{bmatrix}$$ \n",
     "\n",
-    "This is incorrect because it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are **correlated**. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. The **covariance** describes how two variables are correlated. **Covariance** is short for **correlated variances**\n",
-    "\n",
-    "We use a **covariance matrix** to denote **covariances** with multivariate normal distributions, and it looks like this:"
+    "This is incomplete because it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. The *covariance* describes how two variables are correlated. Covariance is short for *correlated variances*."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    " In other words, covariance is a measure for how much variables change together. A couple of examples. Generally speaking as the square footage of a house increases the price increases. These variables are *correlated*, which is also sometimes called *positively correlated*. As the temperature of an automobile's engine increases its life expectancy lowers. These are *inversely correlated* because as one variable gets larger the other variable lowers. This is also called *negatively correlated*. The price of tea and the number of tail wags my dog makes have no relation to each other, and we say they are not correlated - each can change independent of the other.\n",
+    "\n",
+    "Correlation implies *prediction*. If our houses are in the same neighborhood, and yours has twice the square footage of my house I can predict that your house has a higher market price than mine. This is not guaranteed as there are other factors such as proximity to garbage dumps which also affect the price. If my car engine significantly overheats I start planning on replacing it soon. If my dog wags his tail more I don't conclude that tea prices will be increasing.\n",
+    "\n",
+    "For example, here is a plot of of floor plan size vs price for a neighborhood. If a new house comes on the market with a floor plan size of 225 $m^2$ we can estimate its price to be somewhere around $425,000. The correspondence between floor plan area and price is not perfect, but clearly there is enough correlation between them for us to make a reasonable prediction."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8e0b7d62b0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "area = [90, 109, 120, 151, 175, 200, 250, 285, 300]\n",
+    "price = [300000, 350000, 340000, 400000, 400000, 415000, 465000, 480000, 450000]\n",
+    "plt.scatter(area, price, s=80)\n",
+    "plt.title('Floor Plan Area vs. Price')\n",
+    "plt.xlabel('sq meters'); plt.ylabel('price')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We use a *covariance matrix* to denote covariances of a multivariate normal distribution, and it looks like this:\n",
     "$$\n",
     "\\Sigma = \\begin{bmatrix}\n",
     "  \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n",
@@ -335,13 +373,9 @@
     " \\end{bmatrix}\n",
     "$$\n",
     "\n",
-    "If you haven't seen this before it is probably a bit confusing. Instead of starting with the mathematical definition I will build your intuition with thought experiments. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements (covariances) are represent how much the $i$th (horizontal row) and $j$th (vertical column) state variable are linearly correlated to each other. In other words, covariance is a *measure for how much they change together*. \n",
+    "If you haven't seen this before it is probably a bit confusing. Instead of starting with the mathematical definition I will build your intuition with thought experiments. At this point, note that the diagonal contains the variance for each variable, and that all off-diagonal elements (covariances) represent how much the $i$th (horizontal row) and $j$th (vertical column) variables are linearly correlated to each other. So $\\sigma_3^2$ is the variance of the third variable, and $\\sigma_{13}$ is the covariance between the first and third variables.\n",
     "\n",
-    "A couple of examples. Generally speaking as the square footage of a house increases the price increases. These variables are correlated. As the temperature of an engine increases its life expectancy lowers. These are **inversely correlated**. The price of tea and the number of tail wags my dog makes have no relation to each other, and we say they are not correlated - each can change independent of the other.\n",
-    "\n",
-    "Correlation implies *prediction*. If our houses are in the same neighborhood, and you have twice the square footage I can predict that the price is likely to be higher. This is not guaranteed as there are other factors such as proximity to garbage dumps which also affect the price. If my car engine significantly overheats I start planning on replacing it soon. If my dog wags his tail I don't conclude that tea prices will be increasing.\n",
-    "\n",
-    "A covariance of 0 indicates no correlation. So, for example, if the variance for x is 10, the variance for y is 4, and there is no linear correlation between x and y, then we would say\n",
+    "A covariance of 0 indicates no correlation. So, for example, if the variance for x is 10, the variance for y is 4, and there is no linear correlation between x and y, then we would write\n",
     "\n",
     "$$\\Sigma = \\begin{bmatrix}10&0\\\\0&4\\end{bmatrix}$$\n",
     "\n",
@@ -373,16 +407,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
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     "collapsed": false
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    "outputs": [
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x45cc320>"
+       "<matplotlib.figure.Figure at 0x8e09f110b8>"
       ]
      },
      "metadata": {},
@@ -400,7 +434,7 @@
    "source": [
     "This is a plot of two dimensional multivariate Gaussian with a mean of $\\mu=[\\begin{smallmatrix}2\\\\17\\end{smallmatrix}]$ and a covariance of $\\Sigma=[\\begin{smallmatrix}10&0\\\\0&4\\end{smallmatrix}]$. The three dimensional shape shows the probability density of for any value of (x,y) in the z-axis. I have projected the variance for x and y onto the walls of the chart - you can see that they take on the normal Gaussian bell curve shape. The curve for x is wider than the curve for y, which is explained by $\\sigma_x^2=10$ and $\\sigma_y^2=4$. The highest point of the curve is centered over (2, 17), the means for x and y. \n",
     "\n",
-    "All multivariate Gaussians form this shape. If we think of this as a the Gaussian for the position of a dog, the z-value at each point of (x, y) is the probability density of it being at that position. Strictly speaking this is the **joint probability density function**, which I will define soon. So, he has the highest probability of being near (2, 17), a modest probability of being near (5, 14), and a very low probability of being near (10, 10).\n",
+    "All multivariate Gaussians have this shape. If we think of this as a the Gaussian for the position of a dog, the z-value at each point of (x, y) is the probability density of it being at that position. Strictly speaking this is the *joint probability density function*, which I will define soon. So, he has the highest probability of being near (2, 17), a modest probability of being near (5, 14), and a very low probability of being near (10, 10). As with the univariate case this is a *probability density*, not a *probability*. Continuous distributions have an infinite range, and so the probability of being exactly at (2, 17), or any point, is 0%. We can compute the probability of being within a given range by computing the area under the curve. \n",
     "\n",
     "For now we need to understand the following:\n",
     "\n",
@@ -434,7 +468,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -456,7 +490,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -474,7 +508,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
@@ -492,7 +526,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -511,7 +545,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
@@ -537,7 +571,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -545,9 +579,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAr8AAAD9CAYAAAC1Fh+gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x45cc710>"
+       "<matplotlib.figure.Figure at 0x8e09323f98>"
       ]
      },
      "metadata": {},
@@ -565,7 +599,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The result is clearly a 3D bell shaped curve. We can see that the Gaussian is centered around (2,7), and that the probability density quickly drops away in all directions. This plot shows what is known as the **joint probability**. On the sides of the plot I have drawn the **marginal probability** for $x$ and $y$.\n",
+    "The result is clearly a 3D bell shaped curve. We can see that the Gaussian is centered around (2,7), and that the probability density quickly drops away in all directions. This plot shows what is known as the *joint probability*. On the sides of the plot I have drawn the *marginal probability* for $x$ and $y$.\n",
     "\n",
     "It's time to define some terms. The *joint probability*, denoted $p(x,y)$, is the probability of both $x$ and $y$ happening simultaneously.  For example, if you have two die $p(2,5)$ is the probability of the first die rolling a 2 and the second die rolling a 5. Assuming the die are six sided and fair, the probability $p(2,5) = \\frac{1}{6}\\times \\frac{1}{6}=\\frac{1}{36}$. The 3D chart above shows the *joint probability density function*. This means that the area under the curve at any location is proportional to probability of the dog being in that $(x, y)$ position.\n",
     "\n",
@@ -581,16 +615,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7a4ca20>"
+       "<matplotlib.figure.Figure at 0x8e0a11c7f0>"
       ]
      },
      "metadata": {},
@@ -617,7 +651,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -625,9 +659,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7be0d30>"
+       "<matplotlib.figure.Figure at 0x8e0b80d1d0>"
       ]
      },
      "metadata": {},
@@ -660,16 +694,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8225a58>"
+       "<matplotlib.figure.Figure at 0x8e0a246cc0>"
       ]
      },
      "metadata": {},
@@ -693,16 +727,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87282b0>"
+       "<matplotlib.figure.Figure at 0x8e0b7b76d8>"
       ]
      },
      "metadata": {},
@@ -723,8 +757,38 @@
     "$$\n",
     "\\mathbf{\\mu} =\\begin{bmatrix}2\\\\7\\end{bmatrix},\\, \\,\n",
     "\\Sigma = \\begin{bmatrix}2&0\\\\0&2 \\end{bmatrix}\n",
-    "$$ \n",
-    "\n",
+    "$$ "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8e0a246dd8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = [2, 7]\n",
+    "P = [[2, 0], [0, 2]]\n",
+    "plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, \n",
+    "                        title='|2 0|\\n|0 2|')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for $1\\sigma$. As in the univariate case 68% of the data will fall within this ellipse. Recall from the Gaussians chapter the the 68-95-99.7 rule - 68% of all values will fall within 1 standard deviation ($1\\sigma$), 95% within $2\\sigma$, and 99.7% within $3\\sigma$. This rule applies for any dimensional size. The dog could be at (356443, 58483), but the chances for values that far away from the mean are infinitesimally small.\n",
     "\n",
     "A Bayesian way of thinking about this is that the ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. "
@@ -739,8 +803,38 @@
     "$$\n",
     "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n",
     "\\Sigma = \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n",
-    "$$\n",
-    "\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8e0bf0f3c8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = [2, 7]\n",
+    "P = [[2, 0], [0, 9]]\n",
+    "plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, \n",
+    "                        title='|2 0|\\n|0 9|')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "This time we use a different variance for $x$ ($\\sigma_x^2=2$) vs $y$ ($\\sigma^2_y=9$). The result is a tall and narrow ellipse. We can see that a lot more uncertainty in $y$ value vs $x$. Our belief that the value is (2, 7) is the same in both cases, but the uncertainties are different. In this case the standard deviation in $x$ is $\\sigma_x = \\sqrt{2}=1.414$ and the standard deviation for $y$ is $\\sigma_y = \\sqrt{9}=3$. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object or is closer than another sensor, resulting in different uncertainties in each axis."
    ]
   },
@@ -753,13 +847,203 @@
     "$$\n",
     "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n",
     "\\Sigma = \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n",
-    "$$\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8e0a2bc748>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = [2, 7]\n",
+    "P = [[2, 1.2], [1.2, 2]]\n",
+    "plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, \n",
+    "                        title='|2 1.2|\\n|1.2 2|')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This is the first contour that has values in the off-diagonal elements of the covariance, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling us the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow correlated. We denote that in the covariance matrix with values off the diagonal.\n",
     "\n",
-    "This is the first contour that has values in the off-diagonal elements of the covariance, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling us the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal.\n",
+    "Recall the plot for house price vs floor plan area. The plot of price vs area form a slanted grouping of points. We can use NumPy's `cov()` function to compute the covariance of two or more variables by placing them into a 2D array. Let's do that, then plot the covariance ellipse on top of the house data plot."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[  2.23611111e+02,   8.80625000e+05],\n",
+       "       [  8.80625000e+05,   3.68125000e+09]])"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "cov_house = np.cov(np.vstack((area, price)))\n",
+    "cov_house"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8e0a2ab978>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(area, price, s=80)\n",
+    "plt.title('Floor Plan Size vs. Price')\n",
+    "plt.xlabel('sq meters'); plt.ylabel('price')\n",
+    "plot_covariance_ellipse((np.mean(area), np.mean(price)), cov_house, fc='g', \n",
+    "                        alpha=0.2, axis_equal=False, variance=[4])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This should help you form a strong intuition on the meaning and use of covariances. The covariance ellipse shows you how the data is 'scattered' in relation to each other. A narrow ellipse like this tells you that the data is very correlated. There is only a narrow range of prices for any given area. The ellipse leans towards the right, telling us there is a positive correlation - as x increases y also increases. If the ellipse leaned towards the left then the correlation would be negative - as x increases y decreases. We can see this in the following plot:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8e0a1bb1d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "max_temp = [200, 250, 300, 400, 450, 500]\n",
+    "lifespan = [10, 9.7, 5, 5.4, 4.3, 0.3]\n",
+    "plt.scatter(max_temp, lifespan, s=80)\n",
+    "cov = np.cov(np.vstack((max_temp, lifespan)))\n",
+    "plot_covariance_ellipse((np.mean(max_temp), np.mean(lifespan)), cov, fc='g', \n",
+    "            alpha=0.2, axis_equal=False, variance=[4])\n",
+    "plt.title('Engine Temperature vs Lifespan')\n",
+    "plt.xlabel('Temperature (C)'); plt.ylabel('Years');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " When we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how the relative sizes of the variance in $x$ and $y$. For example, a very long and narrow ellipse tilted almost to the horizontal has a strong correlation between $x$ and $y$ (because the ellipse is narrow), and the variance of $x$ is much larger than that of $y$ (because the ellipse is much longer in $x$). Note that in this plot the scales of the x-axis and y-axis are not identical, so the appearence of the plot can be deceiving."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Pearson's Correlation Coefficient\n",
     "\n",
-    "What does this mean in physical terms? Think of parallel parking a car. You can not pull up beside the spot and then move sideways into the space because cars cannot drive sideways. $x$ and $y$ are not independent. This is a consequence of the steering mechanism. When the steering wheel is turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, it cannot vary $x$ and $y$ independently, which means it cannot walk in a straight line or a zig zag. If $x$ changes, $y$ must also change in a defined way. \n",
+    "The correlation between two variables can be given a numerical value with *Pearson's Correlation Coefficient*. It is defined as\n",
     "\n",
-    "When we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how the relative sizes of the variance in $x$ and $y$. For example, a very long and narrow ellipse tilted almost to the horizontal has a strong correlation between $x$ and $y$ (because the ellipse is narrow), and the variance of $x$ is much larger than that of $y$ (because the ellipse is much longer in $x$)."
+    "$$\\rho_{xy} = \\frac{cov(X, Y)}{\\sigma_x \\sigma_y}$$\n",
+    "\n",
+    "This value can range in value from -1 to 1. If the covariance is 0 than $\\rho=0$. A value greater than 0 indicates that the relationship is a positive correlation, and a negative value indicates that there is a negative correlation. Values near -1 or 1 indicate a very strong correlation, and values near 0 indicate a very weak correlation.\n",
+    "\n",
+    "We can use `scipy.stats.pearsonr` function to compute the Pearson coefficient. It returns a tuple of the Pearson coefficient and of the 2 tailed p-value. The latter is not used in this book. Here we compute $\\rho$ for the house price vs area:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.97061425335184115"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from scipy.stats import pearsonr\n",
+    "pearsonr(area, price)[0]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here we compute the correlation between engine temperature and lifespan."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-0.91782234535272555"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pearsonr(max_temp, lifespan)[0]"
    ]
   },
   {
@@ -773,16 +1057,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAAEtCAYAAABTfDVwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x798db38>"
+       "<matplotlib.figure.Figure at 0x8e0a26dc50>"
       ]
      },
      "metadata": {},
@@ -790,8 +1074,6 @@
     }
    ],
    "source": [
-    "import matplotlib.pyplot as plt\n",
-    "\n",
     "P = [[4, 3.9], [3.9, 4]]\n",
     "plot_covariance_ellipse((5, 10), P, edgecolor='k', \n",
     "                        variance=[1, 2**2, 3**2])\n",
@@ -808,16 +1090,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAAFQCAYAAADkwCtvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x79800b8>"
+       "<matplotlib.figure.Figure at 0x8e0a0c60f0>"
       ]
      },
      "metadata": {},
@@ -832,7 +1114,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A word about **correlation** and **independence**. If variables are **independent** they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also **uncorrelated**. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. "
+    "A word about *correlation* and *independence*. If variables are *independent* they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also *uncorrelated*. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. "
    ]
   },
   {
@@ -851,16 +1133,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 24,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAusAAAEWCAYAAADfHdlnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7c0ea90>"
+       "<matplotlib.figure.Figure at 0x8e0bee14a8>"
       ]
      },
      "metadata": {},
@@ -905,7 +1187,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 25,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -913,9 +1195,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAEWCAYAAABL+3CVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAEWCAYAAACpJ2vsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7bc89e8>"
+       "<matplotlib.figure.Figure at 0x8e0a31c9e8>"
       ]
      },
      "metadata": {},
@@ -936,7 +1218,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 26,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -944,9 +1226,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAEWCAYAAABL+3CVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Wl0nOWZ5/9v7VUq7ftSkmzJWrwbL8Q2YIzZ4gRM6IQE\nSBronk5vmZzOTKa7/9MnGeZFesmZc7onc5rOJN2TDkl3lp40hEAImM0Yxza28W5Ziy1rl0r7VnvV\n8/xfGDMQwNhSSSWpfp9zclBUcj2Xbbmen+667uu2mKZpIiIiIiIi18Wa6gJERERERBYjBWkRERER\nkRlQkBYRERERmQEFaRERERGRGVCQFhERERGZAQVpEREREZEZUJAWEREREZmBqwbp/fv3s2fPHnw+\nH1arlSeffPI9j3/9619n5cqVZGZmkp+fzx133MGhQ4fmtGARERERkYXgqkE6EAiwbt06vvWtb+Hx\neLBYLO95vLGxkX/4h3/g7NmzHDhwgOXLl3P33Xfj9/vntGgRERERkVSzXOvJhllZWTzxxBM88sgj\nH/o1k5OT5Obm8uKLL3LnnXcmrUgRERERkYUmaT3S0WiU7373uxQUFLBp06ZkPa2IiIiIyIJkn+0T\nPPfcczz00EMEg0GKior45S9/SX5+fjJqExERERFZsGYdpHft2sWpU6cYHh7mu9/9Lvfeey9Hjhyh\nurr6na+ZmJiY7WVERERERFImJyfnfZ+bdWtHRkYGNTU13HjjjfzTP/0TOTk5fP/735/t04qIiIiI\nLGhJnyOdSCQwDCPZTysiIiIisqBctbUjEAjQ1tYGgGEYdHZ2cvLkSQoKCsjNzeWb3/wme/bsobS0\nlKGhIZ544gn6+vr47Gc/+6HP+UHL4iLX4tixYwBs3rw5xZWILCz6tyHywfRvQ2bro9qTr7oiffTo\nUTZu3MjGjRsJh8M8/vjjbNy4kccffxy73U5TUxP3338/9fX17Nmzh7GxMd544w1Wr16d1N+EiIiI\niMhCc9UV6Z07d161TeOpp55KekEiIiIiIotB0nukRURERETSgYK0iIiIiMgMKEiLiIiIiMyAgrSI\niIiIyAwoSIuIiIiIzICCtIiIiIjIDChIi4iIiIjMgIK0iIiIiMgMKEiLiIiIiMyAgrSIiIiIyAwo\nSIuIiIiIzICCtIiIiIjIDChIi4iIiIjMgIK0iIiIiMgMKEiLiIiIiMyAPdUFiIjIRzNNk+lQlIlA\nhFAkhmGYGKZJwjBp7ZvEArgvDWKzWrBZrVitFrxuBzleNx6XHYvFkurfgojIkqMgLSKyAIxPh+kd\nmmR8OsxEIMJEIPyejyemI8QTUQwjimnGARMTE0yTsbFRAF463wNYsGABiwWLxYHV4sTldJLjdZPj\ndZHjdZOb+fbHmW7yszz4irLJcDtS+vsXEVmMFKRFRObZ+HSYLv8Enf7xt/87wdj0FIlEANOIYJhR\nTCP6vv+6HQkyPSYep4nVamKzgtUKuY4pADwZWZgmJAwwDAvBiIXJoIXJSTsjo04sFicWqxOrxYnV\neuVjNzabl+K8bKqKc6guyaG6NJeq4hyFaxGRj6AgLSIyhxIJg7beUdp6Rn4jNE9f/l98moQxhdMW\npjQvQa7XIMtjkuUxyPSYZGdc/v+ZHgOH7YOvMTQ0AkBR0Qdve4nEYCpkZSpkYTpkZTL49sdhK6NT\nVvzjNtqnM+jsy+SgLRObLet94bqhqpDqkhy1iIiIvIuCtIhIkgXDMc5eGuR0u58z7YNMh0aJx8ff\nE5rL8hOU5ycoL0hQnpcgP8tgrjKqywEuh0FhNkDifY8bBgxOTNE3OkzfqJ3+URsDY+8O11nY7bnk\nZ+ezrraE9bUlNFYV4rB/SLIXEUkTCtIiIkkwNB7g9EU/py76ae0ZIhodIxYfIR4bpTA7xApfnIrC\nuQ/NM2G1QmmeQWmewcbaGPDecN07bKe1z07PgJeB4QJeO56Px53P6mVFrKspYW1NCdleV4p/FyIi\n809BWkRkhsamQhw408Xxtn56hkaJxS4HZ8MYo7ooSqMvRoMvTl6mkepSr9tvhmvThIGxAC29YzT3\nOOgfdXFwMp+j5wtwOPKpLS9kc0M5W1f51FstImlDQVpE5DqYpklz1zD7TnZw6kIf4cgA0dggDusU\ndeUxGn0xVpTH8TjNVJeaVBYLlOUblOVH2Lk2wmQwQEvvFC09vVzyOzndlsv5zhKeeqOEj630sXPD\nMiqLc1JdtojInFKQFhG5BsFwjIPnutl/qpO+YT+RaD9GfJCVlWE21kZZVhLHlkZHXGVnmGypi7Kl\nLko0FqS1L8BbF4a45G/npaMl7D/VxgpfKbeuX8am+jL1U4vIkqQgLSJyFZ0D47x+qpMjzT0EQn6i\nkT68rnFuaYyyaUWUTM/SWnmeCacD1lTHWFMdY3gyxNHWKU60d3OmrYCWrnZys0q4eU0VO9ZXU5iT\nkepyRUSSRkFaROQDtPeN8fSB8zR39hGJ9hONDlBbEuLGhgj15XGsabT6fD0Ksw12bw5z+/owZztD\nHGkdZGAwk18cuMSLR0vZ0ljFnu0NFOd5U12qiMisKUiLiLxL/8gUPz/QzPHWLsKRTmwMsKkmwpa6\nKAXZi2/TYKo4HbBxRZQbaqP0joQ40jrB2a5O3jjZw1stPdyybjn3bKvXtA8RWdQUpEVEgNHJEM8e\nbOHQuQ6CoS7MRB/bGkPctCqM25nq6hYviwV8hQl8hSF2rQ/z2ukQpzv62Xukj4PnurhzUy13banF\n49KkDxFZfBSkRSStBUJRfnXkAq+duMh0sJt4tJuNK0LcuiZMlvqfkyrXa3L/thA3rYrwyskgLX29\n/PyNfvad6uATH6tj54Zl2pQoIovKR3b57d+/nz179uDz+bBarTz55JPvPBaPx/nzP/9z1q9fT2Zm\nJuXl5Xz+85+nu7t7TosWEZmteMLgV2+28Rf/9ArPHTzA6Nib1JW08aVPjnPPlpBC9BwqzjF46NYg\n/+GOEYqzmvAPvcmPX36Dr3/vNQ439WCa+rMXkcXhI1ekA4EA69at49FHH+WRRx7B8q7juAKBACdO\nnOBrX/saGzZsYHx8nK9+9at8/OMf5/Tp09hsWlkQkYWnc2CcJ188RUd/B6HwRWpKprlzQ4iyfPVA\nz6fKogS/c0eAtr4IL5+cpLu/h396boijzTV84c515GV5Ul2iiMhVfWSQ3r17N7t37wbgsccee89j\nOTk57N279z2f+853vsPq1atpbm5m9erVyatURGSW4gmD5w+38fzh8wSCF8hyD/DAbSFqSuOpLi1t\nWSxQXxGnrnyak5civPjWJMfOj3Chd4TP7lzD9jWV71nAERFZSJLeIz0xMQFAXl5esp9aRGTG3r0K\nHQ63cWPdFLdvCOPUTpEFwWKBG2pi1JVN8uyRi7T2jfDPv5rgeJtWp0Vk4UrqLSQajfLVr36VPXv2\nUF5ensynFhGZkQ9ahf7criDLShKpLk0+QKbH5MEdQc50xHj+WECr0yKyoFnM69jVkZWVxRNPPMEj\njzzyvsfi8TgPP/ww58+fZ//+/e9Zkb6ySg3Q1tY2y5JFRK5N/1iQ5471Mjg+gGl2s3H5GLesnMRh\n12a2xSAQtrL3dB4XB/KwWKpZUVbM7o0+sjM0Kk9E5kddXd07H+fk5Lzv8aSsSMfjcR566CHOnTvH\nvn371NYhIil3vH2EvSe7ice7yc0Y4u4bRqksiKa6LLkOXrfBp7aMcL43yCtnQrT1j9P7coDf2rqM\nZcWZqS5PRGT2QToWi/Hggw/S1NTEvn37KC4uvurXb968ebaXlDR17NgxQN9DcnWJhMG/7TvHkY5x\nnM5utq8a584bEjjt719JWCqGhoYAKCoqSnElc6O4GDY1xnj68AiXBuGl87k8WFbNzg3L1OohV6X7\nhszWu7sqPsg1jb+70o5hGAadnZ2cPHmSgoICysvLeeCBBzh27BjPPvsspmkyMDAAQG5uLm63Owm/\nBRGRazMdivLdZ9/ibHsrkUgz931sig01sVSXJUmQ6TH5/K0BXj2d4MD5CP/6UoSeoUkeun0tdttH\nHokgIjInPrJHet++fezatevyF1ss7wzKf+yxx3j88cdZvnz5ez5/xfe///13eqnfneY/qL9E5Fpo\nZUGupndokn945ig9g604LO08eEuAyqL02FC41Fekf9OZDgc/P5yF09XAymV1/OGezWRluFJdlixA\num/IbH1Uhv3IFemdO3diGB9+SMHVHhMRmQ8nLwzwf55/i/GJ8xRl9/PQjgDZGdpQuFStXRYjP2uC\nn+w/x9mLAf7yX0J86VNbqCzWQo2IzC+9HyYii5Zpmjx/uI0nnv41I2PHaazo5XfvnFaITgMVBQn+\n4ONTFGe10+M/wTd//AZvtfSluiwRSTMK0iKyKBmGyQ9ePMW/7z9KIHCCXWuH+PT2IA5bqiuT+ZLp\nMXnsjmnWVPYyOnac//2Lg7x07GKqyxKRNKIzvURk0UkkDL73qxMcOtdEPHqOB3dM0VChY77Tkd0G\nn9oaoiR3iL0nTvHT1wxicYNPbK376F8sIjJLCtIisqjEEwb/+NxbHD3fRDzWxG/fNkVVmmwqlA9m\nscD2lVE8rjGeffM0T+03icYT3HdTg8bjicicUpAWkUUjnjD43784xvGWJox4E4/umsZXqBAtl91Q\nE8NuHeepQ6d57qBJPGHw6R0rFaZFZM4oSIvIohBPGHz32bc43nIOEud57PYpyvI1NUjea+2yGDbr\nOD87eJoX3jSx26xamRaROaPNhiKy4BmGyfeeP8Gx5ibM+HkeVYiWq1hVFeeBmyYIBs/y3MFTPH+4\nLdUlicgSpSAtIguaYZh8/4WTHG46RyLWxG/vmqY0TyFarm5lZZzf2j5BKHiGpw+cZLine truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAEWCAYAAACpJ2vsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7bdb080>"
+       "<matplotlib.figure.Figure at 0x8e0b7d8b38>"
       ]
      },
      "metadata": {},
@@ -970,16 +1252,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 27,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAEWCAYAAABL+3CVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAEWCAYAAACpJ2vsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8bebb00>"
+       "<matplotlib.figure.Figure at 0x8e0a0fd710>"
       ]
      },
      "metadata": {},
@@ -1008,16 +1290,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 28,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAEWCAYAAAAjCPKtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8bfa2e8>"
+       "<matplotlib.figure.Figure at 0x8e0b77fbe0>"
       ]
      },
      "metadata": {},
@@ -1039,16 +1321,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 29,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8cfd9e8>"
+       "<matplotlib.figure.Figure at 0x8e0cf40400>"
       ]
      },
      "metadata": {},
@@ -1079,16 +1361,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 30,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAEWCAYAAACpJ2vsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87c80b8>"
+       "<matplotlib.figure.Figure at 0x8e0cf4d470>"
       ]
      },
      "metadata": {},
@@ -1109,16 +1391,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 31,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARgAAAEWCAYAAAC9hIj8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8c937f0>"
+       "<matplotlib.figure.Figure at 0x8e0b75a2e8>"
       ]
      },
      "metadata": {},
@@ -1163,16 +1445,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 32,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAEWCAYAAACpJ2vsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8cd4630>"
+       "<matplotlib.figure.Figure at 0x8e0b7a8fd0>"
       ]
      },
      "metadata": {},
@@ -1196,16 +1478,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 33,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAEWCAYAAAAjCPKtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7989240>"
+       "<matplotlib.figure.Figure at 0x8e0a0baa58>"
       ]
      },
      "metadata": {},
@@ -1245,16 +1527,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 34,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEmCAYAAADMRU4DAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAAEmCAYAAADIsJ4+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x916c2e8>"
+       "<matplotlib.figure.Figure at 0x8e0b744320>"
       ]
      },
      "metadata": {},
@@ -1275,16 +1557,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 35,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEmCAYAAADMRU4DAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAAEmCAYAAADIsJ4+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7a4cef0>"
+       "<matplotlib.figure.Figure at 0x8e0a1d7898>"
       ]
      },
      "metadata": {},
@@ -1310,16 +1592,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 36,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvUAAAEtCAYAAACIx59SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvcAAAEtCAYAAACMMk9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl0VHWa//FPLakkFZKQkA2SoCBRVLRVIiioLbSAtlv/\nHEcHZGmZbqVtFWR0dJRWaMdtzjgqoh7XFpWlHe1zFJdW2jECHew2MIyCiuyyJWD2pLJW3d8fVbey\nkRiSuqlU5f06h5PUvd8Kj32b5MPDc7/XZhiGIQAAAAARzx7uAgAAAACEBuEeAAAAiBKEewAAACBK\nEO4BAACAKEG4BwAAAKIE4R4AAACIEoR7AAAAIEpEXLhfv369rr76auXk5Mhut+u1117rsGbx4sXK\nzs6W2+3WpEmT9PXXX4ehUgAAAKBvRVy4r6mp0RlnnKGlS5fK7XZ3OP/YY4/piSee0DPPPKOioiJl\nZGRoypQpqq2tDUO1AAAAQN+xRfITahMTE/XMM89o9uzZwWPDhg3T7bffrnvuuUeSVF9fr4yMDD3+\n+OP69a9/Ha5SAQAAAMtFXOe+K3v27FFxcbGmTJkSPBYXF6eLLrpIhYWFYawMAAAAsF5Uhfvi4mLZ\nbDZlZma2OZ6Zmani4uIwVQUAAAD0DWe4CwinysrKcJcAAAAA9FhycnKb11HVuc/KypJhGCopKWlz\nvKSkRFlZWWGqCgAAAOgbURXuR4wYoaysLK1duzZ4rL6+XuvXr9fEiRPDWBkAAABgvYgby6mtrdXO\nnTtlGIZ8Pp++//57/d///Z9SU1OVm5urBQsW6JFHHtEpp5yivLw8/fu//7sSExM1ffr0Lr9u+3/S\nQP9QVFQkScrPzw9zJbAC1zd6cW2jG9c3enFtI0NXo+URF+6Lioo0adIk2Ww2SdIDDzygBx54QHPm\nzNErr7yif/3Xf1V9fb1uvfVWlZeXa/z48fr444+VkJAQ5soBAAAAa0VcuP/pT38qn8/X5Zr7779f\n999/fx9VBAAAAPQPUTVzDwAAAAxkhHsAAAAgShDuAQAAgChBuAcAAACiBOEeAAAAiBKEewAAACBK\nEO4BAACAKEG4BwAAAKIE4R4AAACIEoR7AAAAIEoQ7gEAAIAo4Qx3AQCA6NPY7FVNfXO4ywCAAYdw\nDwAIqdJKj6586FOV1TTo6fIY3fr/xoW7JAAYMBjLAQCE1O9f+0xlNQ2SpHtf+kTl1XVhrggABg7C\nPQAgZAzD0FvrvpEkxcbYVe1p1F827Q5zVQAwcBDuAQAh89XuIzr0Q7XSkmL16yknS5I+/NvOMFcF\nAAMH4R4AEDJ//rs/yJ9/SromnJLuP/bFThmGEc6yAGDAINwDAEKmaPshSdLYkUM0amiiUpPidbi0\nRsVlNWGuDAAGBsI9ACBkvjtQKkk6MWOQbDabTskd4j++vzScZQHAgEG4BwCEhGEY2nGwTJKUm5Yg\nScrL9od78zgAwFqEewBASBz6oVqe+ialJbuV5I6RJJ2cmyqJzj0A9BXCPQAgJMyRnJNzhgSPmZ+b\n5wAA1iLcAwBCwuzOn5xLuAeAcCHcAwBCoqVznxo8Nirb//nOg2Xyen1hqQsABhLCPQAgJHYeLJck\n5bUay0mIdyk7LVFNzT59f6QyXKUBwIBBuAcAhMSh0mpJUk56Upvj5uvDpex1DwBWI9wDAELCfFBV\nVuqgNsfN1zzICgCsR7gHAPSaYRgqKfeH98yUhDbnzNfmeQCAdQj3AIBeK6+uV1OzT0kJsYqPjWlz\nLjOFzj0A9BXCPQCg1zrr2kstYzkl5bV9WhMADESEewBAr3U2by+1BH469wBgPcI9AKDXzK58VkrH\ncM8NtQDQdwj3AIBeM4N7ZmrHsZxMxnIAoM8Q7gEAvWbO3B9rLKd1594wjD6tCwAGGsI9AKDXisv8\nXfnMY4zlDIp3yR0Xo/rGZlV7Gvu6NAAYUAj3AIBe62q3nNbHmbsHAGsR7gEAvVZWVSdJGpLkPuZ5\n83hZdV2f1QQAAxHhHgDQaxU19ZKklMS4Y543j5vrAADWINwDAHqtPBju4495PmWQ/3g5nXsAsBTh\nHgDQK4ZhBEP74EFdd+7Lq+ncA4CVCPcAgF6pa2hWU7NPcS6n4lzOY64xQz9jOQBgLcI9AKBXfqxr\nL7Xq3NcwlgMAViLcAwB6xezGdxnugzP3dO4BwEqEewBAr1R5GiRJyQmxna5JCpzjIVYAYC3CPQCg\nV6pq/eE+qatw7/afM/8iAACwBuEeANArZmA3A7wkFZfXacM3JTIMw38uEPzNvwgAAKxx7G0NAADo\nJnPUJjEQ7vcVV+gf/qNAjc0+HamP08O//pkS412S6NwDgNXo3AMAeqWlc+8P8O8Wbldjs0+S9GbB\nNhmG0WrmnnAPAFYi3AMAeqX9zP27hd8Fz+06VK6v9x5l5h4A+kjUhfslS5bIbre3+TVs2LBwlwUA\nUav1zH1Ts1ef/d9e2WzShadlSJL+sml3cGSnqrYhOIcPAAi9qAv3kjR69GiVlJSouLhYxcXF+uqr\nr8JdEgBELXPUJtEdq/1HqtTU7FNGcpzOGTlEkr9774pxKDbGIa/PUH1jczjLBYCoFpU31DqdTqWn\np4e7DAAYEKoCN9QmuWO161CZJCk71a3sVLckf7iX/GM7Rys8qqptUHxsTHiKBYAoF5Wd+927dys7\nO1sjR47U9OnTtWfPnnCXBABRq/XMvRnkc4a4lTPEDPf+wM/cPQBYL+rC/XnnnadXX31VH330kV56\n6SUVFxdrwoQJKi8vD3dpABCVzLCeGO/S7kC4zx7iVnYg3O8prpDPZ7SZuwcAWCPqxnKmTZvW5vV5\n552nESNGaPny5VqwYEGn7ysqKrK6NPQC1ye6cX0jW8kPFZKkA/t2qWjbbklSzpAEuWOdSh3kUllN\noz74nw2y+fzjO0VbvpJRfShs9SJ0+LMbvbi2/VteXl6n56Kuc9+e2+3W6aefrh07doS7FACISrUN\nTZKkhFinDpR6JCk4b2927w+WepQQ6+8n1dRzQy0AWCXqOvft1dfX69tvv9XkyZO7XJefn99HFeF4\nmJ0Drk904vpGh4bm/5EkTRg/VsVPF0pqCfU/OXm4vtpXoZjEDA0fVit9c0SZw3KVn39m2OpF7/Fn\nN3pxbSNDZWVlp+eirnN/1113ad26ddq7d6/+9re/6dprr5XH49GcOXPCXRoARKXqOv+4TVOzT9We\nRiW6XUp2+3fDGTl0sCRp9+FyJQaeYMvMPQBYJ+o69wcOHNCMGTP0ww8/KD09Xeedd54+//xz5ebm\nhrs0AIg6Pp+hxiavpJb97rNSB8lms0mSMlMGSZJKqzyKc/l/5DQ0MZYDAFaJunC/atWqcJcAAANG\nY7M/2LtiHCqvqZckpSbGB8+nJvk/L6uq14lZyZKkhsBfBgAAoRd1YzkAgL5jdu1dTofKquoktQR6\nSUoZFCdJKquukyvG0eY9AIDQI9wDAHrMHLGJjXGorDoQ7o/Zua9TbAxjOQBgNcI9AKDHgp37mFad\n+9bhPvB5WXWdXM5A576Zzj0AWIVwDwDoMXN+PjbG2dK5TzpG5766TrGBsZyGRsI9AFiFcA8A6LHW\nN9QeaywnOSFONpt/+0uHw97mPQCA0CPcAwB6rKGx1cx9VWC3nFade7vdppRA2Pf6DP97uKEWACxD\nuAcA9Fiwc+9s6dybO+SYzNfmfD675QCAdQj3AIAeaz1zbz55NrlduE9O8L/2+nyB97BbDgBYhXAP\nAOix1rvlVNf5w31ivKvNmkS3/3WzN9C5Z+YeACxDuAcA9Fjrfe7Nzn1SQmybNebrpuZA557dcgDA\nMoR7AECPte7cV3kC4d7dLtwHXgdn7uncA4BlCPcAgB4Lztw7Har2NEqSEjsJ9+ZaZu4BwDqEewBA\nj5ldeKfDrmavT7ExDrkCD6symTP3Dc3slgMAViPcAwB6zNznXjb/h/bz9q2PNTT41zKWAwDWIdwD\nAHrMDOo2mz/dt5+3b32srrFJEg+xAgArEe4BAD1mBnXD//DZDvP2rY95zM494R4ALEO4BwD0WDCo\nB9K9OV/fmrnvfV2D2bnnhloAsArhHgDQY2ZQN8dy4lzODmvMY81e/z73dO4BwDqEewBAj7XM3Ptf\nx8Z0DPexgXAffIgV4R4ALNPxuzAAAN1kPm3W7Ny7nP5tMP/23VF9ta9Co08/M3gs2LlntxwAsAzh\nHgDQY+13y4mNcai2rlEL/1CkxmafTj5pkyaOyQ2sbbmh1jCM4HsAAKHDWA4AoMeCM/eB164Yhz7Z\nvEeNgRGc9z7/LvhQq6Zmn5wOe/BzAEDoEe4BAD3WcnOsf7ec2BiHtu45Ejy/dc+R4Bx+Q5NXsYGg\nz445AGCNbof7l19+WdXV1VbWAgCIMMF97gOvXTEO7TpUFjx/tMITHN1pbPYGu/jsmAMA1uh2uP/1\nr3+trKwsTZ8+XR988IG8Xr4xA8BA17LPvf9DbIxTuw6Vt1lTXFYTXNu6iw8ACL1uh/uioiLdfPPN\nWrduna644goNGzZMCxYs0KZNm6ysDwDQj7V/Qq3L6dDuw/5wPyJjkCTp4NGqwNrmls49O+YAgCW6\nHe7POecc/dd//Zf279+vP//5z5o2bZpeeeUVjRs3TqeddpoeffRR7d+/38paAQD9jBnSfYHWvSvG\nEezUnz58sCSpvKbev7b1zH0jM/cAYIXjvqHWbrdr6tSpeu2111RSUqI33nhDOTk5uu+++zRixAhN\nmjRJy5cvV0NDgxX1AgD6EfPGWMNs3cu/E05cjENpSbGSpCpPQ2CtN7jnPZ17ALBGr3bL2bJli9av\nX6/NmzfLMAyNHj1alZWVuvHGGzVq1Cht2LAhVHUCAPohc+be5/OHe2/gY5I7RknxMLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8c203c8>"
+       "<matplotlib.figure.Figure at 0x8e0cf5b3c8>"
       ]
      },
      "metadata": {},
@@ -1339,16 +1621,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 37,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvUAAAEtCAYAAACIx59SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvcAAAEtCAYAAACMMk9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b36358>"
+       "<matplotlib.figure.Figure at 0x8e0a1fe4a8>"
       ]
      },
      "metadata": {},
@@ -1368,16 +1650,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 38,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvcAAAEtCAYAAACMMk9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87b6e48>"
+       "<matplotlib.figure.Figure at 0x8e0be72cf8>"
       ]
      },
      "metadata": {},
@@ -1399,16 +1681,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 39,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvUAAAEtCAYAAACIx59SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl0XeV5Nvxr731mDUeTNduWbGvyCMZMJiU2ZTBNY5KP\npLw42EDTkATC2JIvtLQ2lAWLN10UWCYU0tLXHwRCmr5JM7BspyVgHJzEBtvY8mxLsq15PJLOfPbe\n3x/P2WewJVuWzihdv7W0ztHZW/KjvbykS7fu596Srus6iIiIiIgoa8npXgAREREREU0NQz0RERER\nUZZjqCciIiIiynIM9UREREREWY6hnoiIiIgoyzHUExERERFlOYZ6IiIiIqIslxWh/rnnnsOVV14J\np9OJ0tJSrF27Fs3Nzeedt2nTJlRVVcHhcGD16tU4dOhQGlZLRERERJRaWRHqP/zwQ3znO9/Brl27\n8P7778NkMuHGG2/E4OBg5Jznn38eL7zwAjZv3ozdu3ejtLQUN910E0ZHR9O4ciIiIiKi5JOy8Y6y\nbrcbTqcT//Vf/4UvfOEL0HUdlZWVeOihh/DEE08AAHw+H0pLS/FP//RPuO+++9K8YiIiIiKi5MmK\nSv25hoeHoWkaCgsLAQAtLS3o7u7GzTffHDnHZrPh+uuvx8cff5yuZRIRERERpURWhvqHH34Yl19+\nOa699loAQFdXFwCgrKws7rzS0tLIMSIiIiKi6cqU7gVcqsceewwff/wxdu7cCUmSLnr+uee4XK5k\nLY2IiIiIKOmcTud5r2VVpf7RRx/Fu+++i/fffx81NTWR18vLywEA3d3dced3d3dHjhERERERTVdZ\nE+offvjhSKCvr6+PO1ZbW4vy8nJs37498prP58POnTuxcuXKVC+ViIiIiCilsqL95oEHHsBbb72F\nn//853A6nZE++by8POTk5ECSJDzyyCN49tln0djYiLq6OjzzzDPIy8vDunXrxv28Y/3pYqbYs2cP\nAGDFihVpXkl24vWbPF67qeH1mxpev8njtZsaXr+p4fW7eAt5VoT6V199FZIk4U//9E/jXt+0aRP+\n4R/+AQDw3e9+F16vFw888AAGBwdxzTXXYPv27cjJyUnHkomIiIiIUiYrQr2maRM6b+PGjdi4cWOS\nV0NERERElFmypqeeiIiIiIjGxlBPRERERJTlGOqJiIiIiLIcQz0RERERUZZjqCciIiIiynIM9URE\nREREWY6hnoiIiIgoyzHUExERERFlOYZ6IiIiIqIsx1BPRERERJTlGOqJiIiIiLIcQz0RERERUZZj\nqCciIiIiynIM9UREREREWY6hnoiIiIgoyzHUExERERFlOYZ6IiIiIqIsx1BPRERERJTlGOqJiIiI\niLIcQz0RERERUZZjqCciIiIiynIM9UREREREWY6hnoiIiIgoyzHUExERERFlOYZ6IiIiIqIsx1BP\nRERERJTlGOqJiIiIiLIcQz0RERERUZZjqCciIiIiynJZE+p37NiBtWvXorq6GrIsY8uWLXHH77nn\nHsiyHPe2cuXKNK2WiIiIiCh1sibUu91uLF26FC+99BLsdjskSYo7LkkSbrrpJnR1dUXe3nvvvTSt\nloiIaJJUFejuBlpbgVAo3ashoixhSvcCJurWW2/FrbfeCkBU5c+l6zosFgtKS0tTvDIiIqIE6e0F\njh8HAoHoazU1aVsOEWWPrKnUX4wkSdi5cyfKysrQ0NCA++67D729veleFhER0cUFAkBzs3iLDfRW\na/rWRERZJWsq9RezZs0a3H777aitrUVLSwuefPJJ3HDDDfjkk09gsVjSvTwiIqKxDQ2JMB8MAooC\nOBzAyAhgNgP86zMRTZCk67qe7kVcqry8PLzyyivYsGHDuOd0dnZi7ty5ePfdd/HlL3858rrL5Yo8\nP378eFLXSUREdCHmnh5Yz5yBBCCUnw9/RQUcJ05AUlV4a2sRKipK9xKJKEPU1dVFnjudzvOOT5tK\n/bkqKipQXV2NEydOpHspRERE8XQd1rY2WPr7AQD+sjIEqqpgP3kSkqoi5HQy0BPRJZm2ob63txft\n7e2oqKgY95wVK1akcEWZZc+ePQBm9jWYCl6/yeO1mxpev6nJiOtn9M+XlIj2msZG8djaCrjdQHU1\ncOWVGddPnxHXLovx+k0Nr198t8lYsibUu93uSLuMpmloa2vDvn37UFxcjKKiImzcuBFf+cpXUF5e\njtbWVjzxxBMoKyuLa70hIiJKq9FR4OBBwOcToX3xYiAvT0y9aW0FJAlYtCjjAj0RZb6smX6ze/du\nLF++HMuXL4fP58PGjRuxfPlybNy4EYqi4ODBg7jtttvQ0NCAe+65B01NTdi1axdycnLSvXQiIiKg\npwfYu1cEeqcTuOIKEehHR4EjR8Q58+cDhYXpXScRZaWsqdSvWrUKmqaNe3zr1q0pXA0REdElaGkB\n2trE84oKoK4OkGUx8ebgQXHDqfJy0XpDRDQJWRPqiYiIso6qAocOAf39orVmwQKgqkoc03XRW+/z\nAfn5QH19etdKRFmNoZ6IiCgZvF5RhXe7xcz5hQvjW2uOHxcz6o3eejlrOmKJKAMx1BMRESWayyUC\nfTAI5OSI0G63R493dIg3WRbHeJNEIpoihnoiIqJE6u8XbTWaBhQXiwq9okSPDw2JKj0ANDSIzbJE\nRFPEUE9ERJQonZ3AsWOiX76yUmyIlaTocZ9PBH5dB2bPBsrK0rdWIppW2MBHREQJ0+fyIBBU072M\n9GhrA44eFYG9pkZsfI0N9KoabckpKgLmzUvbUolo+mGlnoiIEuJE+wDO9g5DkSVcs7AaZpNy8Q+a\nDnRdtNN0dIgQX1cnqvTnnnPkiJhJ73CIlpzYwE9ENEWs1BMRUUL0DLoBAKqmo3/Ym+bVpIimiZGV\nxqbXRYvOD/QAcOKEuGusySQ2xppYUyOixGKoJyKiKRt2+xEIRdtu+lyeNK4mRUIh4LPPomF92TKg\npOT8806fBtrbo5NuHI7Ur5WIpj2GeiIimrKhUR8AoMTpiHt/2vL7gb17o3PmL78ccDrPP6+rCzh1\nSrTaNDUBBQWpXysRzQgM9URENGVefxAAUJxvh0mREVI1BEPTdMOsxyMCvdstZtAvXy4ez9XfLzbO\nAqLPftas1K6TiGYUhnoiIpoybyAEALBZTLBbRL+41x9K55KSY3hYBHqfT1TmL79cVOrHOu/QIbFB\ndu7csfvsiYgSiKGeiIimzKjU261m2K3muNemjf5+YN8+MZKypET00I+14dXjAQ4cECMsKyqA2trU\nr5WIZhxuvycioinRNB3+oAoJgNWswBau1PsC06hS390tRlLqugjq586gN/j9YvNsMCjuJltfn/q1\nEtGMxFBPRERT4otpvZEkCXZruP1muoT6s2fFSEpAtNKMV3kPhUSF3ucD8vPFeEvOoieiFGGoJyKi\nKYltvYl9nBbtN62t4g0A5s8HZs8e+zxNE3eLNW4utWSJGGFJRJQiDPVERDQlsZX62Mesb785flzM\nl5ckoKEBKC8f+zxdBw4fjo63XLoUMJtTu1YimvEY6omIaEqMNhuj7cZqViBLEvxBFZqmQ5azrAXF\nCOk9PaLavnDh2DeVMsTeLXbpUsBmS91aiYjCGOqJiGhKjHn0FpMCAJAkCWaTDH9QRTCkwmrJoh81\nqgo0NwMDAyKkL14s+uNbWoCODqCwUIR8Q2tr/N1ix5pXT0SUAln0nZaIiDJRSNUAACYl2kNuUkSo\nD6kaxpjinpmMja4ul2ifWbpUvLZ7N+D1inMGBqLnt7eLUC9JIujzbrFElEYM9URENCXBkAj15nCl\nHogG/GA48Ge8QADYv1/cJdZmE4G+pye6SdZQUSEeu7tFzz0g+u0v1J5DRJQCDPVERDQlY1XqjYAf\nyoZQ7/WK2fJer2ifWbRItNv09ooqvCyLthybDaipEdX6I0fEx86fP/4GWiKiFOK8LSIimhKjp95s\nim+/iT2WsUZHgb17RaDPzwcaG4FDh6IbX6uqxLhKQNxIanRUjK7UdWDOnPFHXBIRpRhDPRERTcmY\nlfrw84yu1LtcwL59ovWmsFDcWOqzz6Kz5puaRJuNrotjVqvoudc00YYzb166vwIiogi23xAR0aSF\nVA06RKCXYu6easr0UD8wICrumgbMmgU4ndEKfFGR6JP/7DMgGBT98uXloqIfConz6+vT/RUQEcVh\nqCciokkbq0oPRHvqjU20mcQ0NBQN9OXlom/+xAlxcM4coLZWjLV0u0WP/fz5IuAbFf2mJvExREQZ\nhO03REQ0aUbP/LmhPlMr9aaBAdhOnoy20AQCQGen2Azb1CRaalpbgb4+MdaysVEEfKPnfvFicS4R\nUYZhpZ6IiCZN1XQAWRLqu7pga2mBBIhAPzoKjIwAFguwZAmQlyfGWLa1iUp8Q4Oo4Bs99kuWAIpy\nsX+FiCgtGOqJiGjS1HBoV2QJbm8Ax872oyjPjoJcmziuZUio7+gAjh2DBCBQXAwMDYnqu90uZtLb\n7SK8Hz0qzp83T3yMyyVGWS5bJir3REQZKmv+hrhjxw6sXbsW1dXVkGUZW7ZsOe+cTZs2oaqqCg6H\nA6tXr8ahQ4fSsFIiopkjtqf+TO8wXG4/WrqGoIUr+BlRqT97Fjh2DIAI9CaXSwT6vDzg8stFoPf5\nxGQbVY1W8QcGoneWtWbNfXGJaIbKmlDvdruxdOlSvPTSS7Db7XFTFgDg+eefxwsvvIDNmzdj9+7d\nKC0txU033YTR0dE0rZiIaPoz2m9kSUK/yxN5fXDUF3c8bU6fjm6CnTUL5sFByKGQmHBz2WWi9SYY\nFBth/X6goECc290tWm2WLhWtN0REGS5rQv2tt96KZ555BrfffjvkczYp6bqOF198ELine truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7bff6d8>"
+       "<matplotlib.figure.Figure at 0x8e0bedd358>"
       ]
      },
      "metadata": {},
@@ -1430,18 +1712,18 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This is a *key point* in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). This is called an **observed variable**. It does not have a sensor that provides velocity. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity a **hidden variable**. Hidden means what it sounds like - there is no sensor that is measuring velocity, thus its value is hidden from us. We are able to use the correlation between position and velocity to infer its value very accurately.\n",
+    "This is a key point in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). This is called an *observed variable*. It does not have a sensor that provides velocity. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity a *hidden variable*. Hidden means what it sounds like - there is no sensor that is measuring velocity, thus its value is hidden from us. We are able to use the correlation between position and velocity to infer its value very accurately.\n",
     "\n",
-    "To round out the terminology there are also **unobserved variables**. For example, the aircraft's state includes things such as as heading, engine RPM, weight, color, the first name of the pilot, and so on. We cannot sense these directly using the position sensor so they are not *observed*. There is no way to *infer* them from the sensor measurements and correlations (red planes don't go faster than white planes), so they are not *hidden*. Instead, they are **unobservable**. If you include an unobserved variable in your filter state the estimate for that variable will be nonsense."
+    "To round out the terminology there are also *unobserved variables*. For example, the aircraft's state includes things such as as heading, engine RPM, weight, color, the first name of the pilot, and so on. We cannot sense these directly using the position sensor so they are not *observed*. There is no way to *infer* them from the sensor measurements and correlations (red planes don't go faster than white planes), so they are not *hidden*. Instead, they are *unobservable*. If you include an unobserved variable in your filter state the estimate for that variable will be nonsense."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the measurement of the position is not in the direction of the  velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. \n",
+    "What makes this possible? Imagine for a moment that we superimposed the velocity from a different airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the measurement of the position is not in the direction of the velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. \n",
     "\n",
-    "It is important to understand that we are taking advantage of the fact that velocity and position are correlated. We get a rough estimate of velocity from the distance and time between two measurement, and use Bayes theorem to and produce very accurate estimates after only a few observations. Please reread this section if you have any doubts. If you grasp this point the rest is straightforward. If you do not you will quickly find it impossible to reason about what you will learn in the rest of this chapter."
+    "It is important to understand that we are taking advantage of the fact that velocity and position are correlated. We get a rough estimate of velocity from the distance and time between two measurement, and use Bayes theorem to and produce very accurate estimates after only a few observations. Please reread this section if you have any doubts. If you do not understand this you will quickly find it impossible to reason about what you will learn in the following chapters."
    ]
   },
   {
@@ -1485,7 +1767,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.5.0"
   }
  },
  "nbformat": 4,