{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"2D Data Plots and Analysis\n",
"===\n",
"\n",
"## Unit 7, Lecture 4\n",
"\n",
"*Numerical Methods and Statistics*\n",
"\n",
"----\n",
"\n",
"#### Prof. Andrew White, Feburary 27th 2018"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import random\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from math import sqrt, pi\n",
"import scipy\n",
"import scipy.stats\n",
"\n",
"plt.style.use('seaborn-whitegrid')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Working with 2D data\n",
"===\n",
"\n",
"Now we'll consider 2D numeric data. Recall that we're taking two measurements simultaneously so that their should be an equal number of data points for each dimension. Furthermore, they should be paired. For example, measuring people's weight and height is valid. Measuring one group of people's height and then a different group of people's weight is not valid."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Our example for this lecture will be one of the most famous datasets of all time: the Iris dataset. It's a commonly used dataset in education and describes measurements in centimeters of 150 Iris flowers. The measured data are the columns and each row is an iris flower. They are sepal length, sepal width, pedal length, pedal width, and species. We'll ignore species for our example."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Flower Anatomy\n",
"---\n",
""
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"import pydataset\n",
"\n",
"data = pydataset.data('iris').values\n",
"#remove species column\n",
"data = data[:,:4].astype(float)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Sample Covariance\n",
"===\n",
"\n",
"Let's begin by computing sample covariance. The syntax for covariance is similar to the `std` syntax for standard deviation. We'll compute the sample covariance between petal width and sepal width."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.18997942, -0.12163937],\n",
" [-0.12163937, 0.58100626]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.cov(data[:,1], data[:,3], ddof=1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"This is called a **covariance matrix**:\n",
"\n",
"$$\\left[\\begin{array}{lr}\n",
"\\sigma_{xx} & \\sigma_{xy}\\\\\n",
"\\sigma_{yx} & \\sigma_{yy}\\\\\n",
"\\end{array}\\right]$$\n",
"\n",
"The diagonals are the sample variances and the off-diagonal elements are the sample covariances. It is symmetric, since $\\sigma_{xy} = \\sigma_{yx}$. The value we observed for sample covariance is negative covariance the measurements. That means as one increases, the other decreases. The `ddof` was set to 1, meaning that the divosor for sample covariance is $N - 1$. Remember that $N$ is the number of *pairs* of $x$ and $y$ values. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The covariance matrix can be any size. So we can explore all possible covariances simultaneously. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.68569351, -0.042434 , 1.27431544, 0.51627069],\n",
" [-0.042434 , 0.18997942, -0.32965638, -0.12163937],\n",
" [ 1.27431544, -0.32965638, 3.11627785, 1.2956094 ],\n",
" [ 0.51627069, -0.12163937, 1.2956094 , 0.58100626]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#add rowvar = False to indicate we want cov\n",
"#over our columns and not rows\n",
"np.cov(data, rowvar=False, ddof=1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"To read this larger matrix, recall the column descriptions: sepal length (0), sepal width (1), pedal length (2), pedal width (3). Then use the row and column index to identify which sample covariance is being computed. The row and column indices are interchangable because it is symmetric. For example, the sample covariance of sepal length with sepal width is $-0.042$ centimeters."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Scatter Plot\n",
"----\n",
"\n",
"To get a better sense of this data, we can use a scatter plot. Let's see a high positive sample covariance and a low positive sample covariance. Sepal length and pedal length have a high positive sample covariance and sepal width with pedal width has a low positive sample covariance."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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\n",
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