p
hw3-firstname-lastname-1-3e5llpab.ipyn
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Homework Week 3 \n",
"\n",
"\n",
"From Week 3, please submit your homework to iCollege -> assignment -> find your TA's folder -> sub folder of week 3.\n",
"\n",
"
Deadline: Sep 19th 2020 11:59PM\n",
"\n",
"## Please change this Jupyter Notebook title with your first name and last name before you submit your homework. No initials please! For example, HW3-Jingjing-Cannon \n"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from scipy.optimize import curve_fit \n",
"import numpy as np\n",
"from statistics import mean"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Find the best cureve that fits the data points from the equation below, with the best fit coeffints ([w]) and interception(b). \n",
"$$\n",
"\\begin{equation}\n",
"y = -0.5 + 2.2 \\times x + 0.3 \\times x^3+ 2 \\times N\n",
"\\end{equation}\n",
"$$\n",
" N = 100 random numbers that follow normal distribution \n",
" x = 100 numbers evenly spaced between (-5,5)\n",
"\n",
" Print your coefficeint(s) and intercept.\n",
"\n",
" Plot a smooth predicted line from your fitted model together with the observed data points from the equation above, the line and the points should be in different colors.\n",
" \n",
" Hint: 2 X N is introducing some tiny noise into the data."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"X=np.linspace(-5,5,100)\n",
"N=np.random.normal(size=100)\n",
"y= -0.5 + 2.2 * X + 0.3 * (X**3) + 2* N"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"def fit_slope_and_intercept(X,y):\n",
" m = (((mean(X)*mean(y)) - mean(X*y)) /\n",
" ((mean(X)*mean(X)) - mean(X*X)))\n",
" \n",
" b = mean(y) - m*mean(X)\n",
" \n",
" return m, b"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6.794364360802028 -0.7369480089956683\n"
]
}
],
"source": [
"coeff, inter = fit_slope_and_intercept(X,y)\n",
"print(coeff, inter)"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
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" ...