\n"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import chi2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's start by simulating a data set with some polynomial plus noise. We will use numpy.polyval() to generate the polynomial: you get to choose what order you want by setting the number of input parameters (choose something between 3 and 6)."
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
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