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‎.ipynb_checkpoints/Untitled1-checkpoint.ipynb

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{
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"metadata": {
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"name": "",
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"signature": "sha256:24d12ab64e5e93c82e0acf22e043d94d7006b033acc4160a5a99e702b6873929"
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": []
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}

‎.ipynb_checkpoints/scipy_fitting_trendline-checkpoint.ipynb

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{
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"metadata": {
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"name": "",
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"signature": "sha256:d274a9480a3c582c98c551412b6b8f6d82e57bc95757b304c6c65df44b6d6e71"
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": [
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Finding A Trend Line Of Data\n",
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"\n",
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"This snippit was written by [Chris R. Albon](http://www.chrisralbon.com/) and is part of his collection of [well-documented Python snippits](https://github.com/chrisalbon/code_py). All code is written in Python 3 in iPython notebook and offered under the [Creative Commons Attribution-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-sa/4.0/).\n",
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"\n",
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"Based on: SciPy And NumPy"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Import modules"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"import numpy as np\n",
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"from scipy.optimize import curve_fit"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 3
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Creating some clean data"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"# create a function called func(),\n",
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"def func(x, a, b):\n",
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" # that multiplies a and x, then adds b\n",
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" return a * x + b"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 7
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"# create 100 elements, evenly spaced between 0 and 10\n",
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"x = np.linspace(0, 10, 100)\n",
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"\n",
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"# mix up the data by applying func()\n",
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"y = func(x, 1, 2)\n",
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"\n",
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"# view the first few entries\n",
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"y[0:10]"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 18,
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"text": [
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"array([ 2. , 2.1010101 , 2.2020202 , 2.3030303 , 2.4040404 ,\n",
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" 2.50505051, 2.60606061, 2.70707071, 2.80808081, 2.90909091])"
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]
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}
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],
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"prompt_number": 18
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Add noise to the data"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"# Add some randomness to the data by multiplying y by 100 values drawn from the normal distribution\n",
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"yn = y + 0.9 * np.random.normal(size=len(x))\n",
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"\n",
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"# view the first few entries\n",
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"yn[0:10]"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 20,
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"text": [
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"array([ 3.63606696, 3.51496281, 2.68882029, 2.11995938, 2.36446115,\n",
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" 3.41454019, 1.66117548, 2.59706936, 3.22359943, 2.16499171])"
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]
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}
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],
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"prompt_number": 20
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Fitting a line to the data\n",
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"\n",
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"- func = the model function\n",
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"- x = the independent variable\n",
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"- y = the dependent variable"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"# return an array of values (popt) so that the squared error of the line is minimized\n",
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"# also return a 2d array with eh covariance of popt\n",
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"popt, pcov = curve_fit(func, x, yn)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 25
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### What is popt?\n",
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"\n",
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"popt returns the values of x (the independent variable) and yn (the dependent variable) with the smallest squared error"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"popt"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 26,
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"text": [
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"array([ 0.92825153, 2.25863607])"
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]
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}
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],
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"prompt_number": 26
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This means that if x = 0.92 and y = 2.25, the function (called func()) best fits the data"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [],
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"language": "python",
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"metadata": {},
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"outputs": []
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}
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],
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"metadata": {}
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}
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]
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}

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