1358 lines
317 KiB
Plaintext
1358 lines
317 KiB
Plaintext
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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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"# Рабочая тетрадь No 4"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 478,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"from sklearn import metrics\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy.optimize import curve_fit\n",
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"from sklearn.linear_model import LinearRegression\n",
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"from sklearn.model_selection import train_test_split"
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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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"### 1.1.3 Задание\n",
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"\n",
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"Представьте собственные данные и постройте эктраполяцию полиномами \n",
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"первой, второй и третьей степени. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 479,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[-5.1585996 -4.46639064 -2.55830037 -2.0590825 -0.53638287 0.3553611\n",
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" 0.60294719 2.45189108 3.28141706 4.08769096 4.92161744]\n",
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"[24.70826208 16.36113899 9.04877285 4.01427977 1.02983411 0.38854345\n",
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" 0.74865966 4.11727242 9.13843478 15.83010792 24.60875347]\n"
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]
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}
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],
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"source": [
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"delta = 1.0\n",
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"x = np.linspace(-5, 5, 11)\n",
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"y = x ** 2 + delta * (np.random.rand(11) - 0.5)\n",
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"x += delta * (np.random.rand(11) - 0.5)\n",
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"\n",
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"print(x)\n",
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"print(y)"
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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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"#### Эктраполяция полиномом первой степени"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 480,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAAh8AAAGdCAYAAACyzRGfAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy80BEi2AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAk9ElEQVR4nO3df3BU5d338c9ustkQTfCOSEJugkYapK0jzK2CjD40CAk/OrYo01rtTIE6dGQCCGlHxalCtDN0rAOKpWj7tGKrVKdOkWoRWWOB8SlUxVJHO/wIhYpAELibbEhgc0j2+SPZzW52E3bDnmt/vV8zO2TPnux+80327IfrXOcch9/v9wsAAMAQZ7ILAAAA2YXwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMCo3GQX0FdXV5eOHz+uwsJCORyOZJcDAABi4Pf71draqrKyMjmdA49tpFz4OH78uMrLy5NdBgAAGISjR49q5MiRA66TcuGjsLBQUnfxRUVFSa4mdVmWpW3btqmmpkYulyvZ5WQkemw/emw/emwv+tvL6/WqvLw8+Dk+kJQLH4FdLUVFRYSPAViWpYKCAhUVFWX9H7xd6LH96LH96LG96G+kWKZMMOEUAAAYRfgAAABGET4AAIBRhA8AAGAU4QMAABgVV/hYtWqVbr75ZhUWFmr48OGaPXu29u/fH7ZOVVWVHA5H2O3+++9PaNEAACB9xRU+duzYodraWu3evVsej0eWZammpkZtbW1h6y1YsEAnTpwI3p588smEFg0AANJXXOf52Lp1a9j9DRs2aPjw4dqzZ48mT54cXF5QUKDS0tLEVJhAaxsOao3ngJZVj9GSqZXJLgcAgKx0SScZa2lpkSQVFxeHLX/55Zf10ksvqbS0VHfccYceffRRFRQURH0On88nn88XvO/1eiV1n7jFsqxLKS/Mz/9ySM+8e0iStNpzQJ2dnVo0ZXTCnt+0QG8S2SOEo8f2o8f2o8f2or+94umBw+/3+wfzIl1dXfrGN76h5uZmvffee8Hlv/zlL3X11VerrKxMH3/8sR566CFNmDBBf/zjH6M+z8qVK1VfXx+xfOPGjf0Glni9/blDW47mRCyfVd6p6SMH9eMDAJAWuj8DnZpV3mXrZ157e7vuvfdetbS0XPQM5YMOHwsXLtRbb72l9957b8ALyLz77ruaOnWqGhsbNXp05EhDtJGP8vJynT59OiGnVw8d8YjmgdtHp+UIiGVZ8ng8qq6u5pS+NqHH9qPH9qPH9kr1/vb9DLTzM8/r9WrYsGExhY9B7XZZtGiR3nzzTe3cufOiV66bOHGiJPUbPtxut9xud8Ryl8t1yb/ItQ0HBwwekvTMu4eUk5OTtnNAEtEnDIwe248e248e2ysV+xvtM9DOz7x4fv64woff79fixYu1adMmbd++XRUVFRf9nr1790qSRowYEc9LXbK1DQe12nMgpnUD66VrAAEAINRAn4Gp8JkX16G2tbW1eumll7Rx40YVFhaqqalJTU1NOnfunCTp0KFDeuKJJ7Rnzx4dOXJEf/rTn/S9731PkydP1g033GDLD9CfNTEGj8GuDwBAKorlP9+rPQe0tuGgoYoixRU+1q9fr5aWFlVVVWnEiBHB26uvvipJysvL0zvvvKOamhqNHTtWP/zhDzVnzhy98cYbthQ/kGXVY2xdHwCAVBPvqH+yAkjcu10GUl5erh07dlxSQYkSGE6K5ZdQx3k/AAAZYDCj/sn4/Mvoa7ssmVqpuouMaBA8AACZIl1G/TM6fEgDBxCCBwAgk8Tyn+6AZH4GZnz4kKL/MggeAIBMlA6j/pd0evV0Emgy13YBAGS6geY9Jjt4SFkUPqTuX0ayGw4AgAnRAkgqBA8py8IHAADZJFVH/QkfAABksFQc9c+KCacAACB1ED4AAIBRhA8AAGAU4QMAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRhA8AAGAU4QMAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRhA8AAGAU4QMAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRhA8AAGAU4QMAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRhA8AAGBUXOFj1apVuvnmm1VYWKjhw4dr9uzZ2r9/f9g658+fV21tra688kpdfvnlmjNnjk6ePJnQogEAQPqKK3zs2LFDtbW12r17tzwejyzLUk1Njdra2oLrLFu2TG+88Yb+8Ic/aMeOHTp+/LjuuuuuhBcOAADSU248K2/dujXs/oYNGzR8+HDt2bNHkydPVktLi379619r48aNuv322yVJL7zwgr785S9r9+7duuWWWxJXOQAASEuXNOejpaVFklRcXCxJ2rNnjyzL0rRp04LrjB07VqNGjdKuXbsu5aUAAECGiGvkI1RXV5eWLl2qW2+9Vddff70kqampSXl5ebriiivC1i0pKVFTU1PU5/H5fPL5fMH7Xq9XkmRZlizLGmx5GS/QG3pkH3psP3psP3psL/rbK54eDDp81NbW6pNPPtF777032KeQ1D2Jtb6+PmL5tm3bVFBQcEnPnQ08Hk+yS8h49Nh+9Nh+9Nhe9Fdqb2+Ped1BhY9FixbpzTff1M6dOzVy5Mjg8tLSUnV0dKi5uTls9OPkyZMqLS2N+lzLly9XXV1d8L7X61V5eblqampUVFQ0mPKygmVZ8ng8qq6ulsvlSnY5GYke248e248e24v+9grsuYhFXOHD7/dr8eLF2rRpk7Zv366Kioqwx2+88Ua5XC41NDRozpw5kqT9+/frs88+06RJk6I+p9vtltvtjljucrmy/hcZC/pkP3psP3psP3psL/qruH7+uMJHbW2tNm7cqM2bN6uwsDA4j2Po0KEaMmSIhg4dqvvuu091dXUqLi5WUVGRFi9erEmTJnGkCwAAkBRn+Fi/fr0kqaqqKmz5Cy+8oHnz5kmS1qxZI6fTqTlz5sjn82n69On6xS9+kZBiAQBA+ot7t8vF5Ofna926dVq3bt2giwIAAJmLa7sAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAowochaxsOquLhP2ttw8FklwIAQFLlJruAbLC24aBWew5IUvDfJVMrk1kSAABJw8iHzUKDR8BqzwFGQAAAWYvwYaNowSOAAAIAyFaED5sMFDwCCCAAgGxE+LBBLMEjgAACAMg2hA8brIkxeAx2fQAA0hnhwwbLqsfYuj4AIDVxWoXYcKitDQKH0cay66WuegyH3QJABuC0CrEjfNgklgBC8ACAzPDzvxzSM+8eCltGAOkf4cNGAwUQggcAZIa3P3doy9FDUR8jgETHnA+bLZlaqbo+czoIHgCQGX7+l0PacjRnwHU4qjESIx8GBILGGs8BLSN4AEBGWNtwMGJXS38YAQlH+DBkydRK/ugAIIMM5rQKfA50Y7cLAACDwGkVBo/wAQDAICyZWqkHbh8d07rM9QtH+AAAYJAWTRmtWeWdA65D8IhE+AAA4BJMH+nvdwSE4BEd4QMAgEu0aMpoTqsQB452AQAgATitQuziHvnYuXOn7rjjDpWVlcnhcOj1118Pe3zevHlyOBxhtxkzZiSqXgAAUtaSqZU6/NOvEzwuIu7w0db
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"m = np.vstack((x, np.ones(11))).T\n",
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"s = np.linalg.lstsq(m,y,rcond = None)[0]\n",
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"\n",
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"x_prec = np.linspace(-5, 5, 101)\n",
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"\n",
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"plt.plot(x, y,'D')\n",
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"plt.plot(x_prec, s[0] * x_prec + s[1], '-', lw=1)\n",
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"plt.grid()"
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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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"#### Эктраполяция полиномом второй степени"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 481,
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"metadata": {},
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"outputs": [
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{
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"data": {
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|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"m = np.vstack((x**2, x, np.ones(11))).T\n",
|
|||
|
|
"s = np.linalg.lstsq(m, y, rcond = None)[0]\n",
|
|||
|
|
"\n",
|
|||
|
|
"x_prec = np.linspace(-5, 5, 101)\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.plot(x, y,'D')\n",
|
|||
|
|
"plt.plot(x_prec, s[0] * x_prec**2 + s[1] * x_prec + s[2], '-', lw=2)\n",
|
|||
|
|
"plt.grid()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Эктраполяция полиномом третьей степени"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 482,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"m = np.vstack((x**3, x**2, x, np.ones(11))).T\n",
|
|||
|
|
"s = np.linalg.lstsq(m, y, rcond = None)[0]\n",
|
|||
|
|
"\n",
|
|||
|
|
"x_prec = np.linspace(-5, 5, 101)\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.plot(x, y,'D')\n",
|
|||
|
|
"plt.plot(x_prec, s[0] * x_prec**3 + s[1] * x_prec**2 + s[2] * x_prec + s[3], '-', lw=3)\n",
|
|||
|
|
"plt.grid()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### 1.1.5 Задача\n",
|
|||
|
|
"\n",
|
|||
|
|
"Необходимо проверить гипотезу, что наши точечно заданная функция ложится \n",
|
|||
|
|
"на кривые вида: \n",
|
|||
|
|
"1. $f(x,b) = b_0+b_1x$\n",
|
|||
|
|
"2. $f(x,b) = b_0+b_1x+b_2x^2$\n",
|
|||
|
|
"3. $f(x,b) = b_0+b_1\\ln(x)$\n",
|
|||
|
|
"4. $f(x,b) = b_0x^{b_1}$ "
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Функция №1"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 483,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[1.2474115 1.73859228]\n",
|
|||
|
|
"0.0001438268762724966\n",
|
|||
|
|
"0.12646845774981774\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"beta = (1.24, 1.74)\n",
|
|||
|
|
"def f(x, b0, b1):\n",
|
|||
|
|
" return b0 + b1 * x\n",
|
|||
|
|
"\n",
|
|||
|
|
"xdata = np.linspace(0,5,50)\n",
|
|||
|
|
"y = f(xdata, *beta)\n",
|
|||
|
|
"ydata = y + 0.05 * np.random.randn(len(xdata))\n",
|
|||
|
|
"\n",
|
|||
|
|
"from scipy.optimize import curve_fit\n",
|
|||
|
|
"beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
|
|||
|
|
"print(beta_opt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"lin_dev = sum(beta_cov[0])\n",
|
|||
|
|
"print(lin_dev)\n",
|
|||
|
|
"\n",
|
|||
|
|
"residuals = ydata - f(xdata, *beta_opt)\n",
|
|||
|
|
"fres = sum(residuals**2)\n",
|
|||
|
|
"print(fres)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 484,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"fig, ax = plt.subplots()\n",
|
|||
|
|
"ax.scatter(xdata, ydata)\n",
|
|||
|
|
"ax.plot(xdata, y, 'r', lw=2)\n",
|
|||
|
|
"ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
|
|||
|
|
"ax.set_xlim(0,5)\n",
|
|||
|
|
"ax.set_xlabel(r'$x$', fontsize=18)\n",
|
|||
|
|
"ax.set_ylabel(r'$f(x, \\beta)$', fontsize=18)\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Функция №2"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 485,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[0.53903101 2.70563694 1.17692555]\n",
|
|||
|
|
"0.00014584672644415915\n",
|
|||
|
|
"0.12162090612880988\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"beta = (0.51, 2.74, 1.17)\n",
|
|||
|
|
"def f(x, b0, b1, b2):\n",
|
|||
|
|
" return b0 + b1 * x + b2 * x**2\n",
|
|||
|
|
"\n",
|
|||
|
|
"xdata = np.linspace(0,5,50)\n",
|
|||
|
|
"y = f(xdata, *beta)\n",
|
|||
|
|
"ydata = y + 0.05 * np.random.randn(len(xdata))\n",
|
|||
|
|
"\n",
|
|||
|
|
"from scipy.optimize import curve_fit\n",
|
|||
|
|
"beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
|
|||
|
|
"print(beta_opt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"lin_dev = sum(beta_cov[0])\n",
|
|||
|
|
"print(lin_dev)\n",
|
|||
|
|
"\n",
|
|||
|
|
"residuals = ydata - f(xdata, *beta_opt)\n",
|
|||
|
|
"fres = sum(residuals**2)\n",
|
|||
|
|
"print(fres)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 486,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"fig, ax = plt.subplots()\n",
|
|||
|
|
"ax.scatter(xdata, ydata)\n",
|
|||
|
|
"ax.plot(xdata, y, 'r', lw=2)\n",
|
|||
|
|
"ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
|
|||
|
|
"ax.set_xlim(0,5)\n",
|
|||
|
|
"ax.set_xlabel(r'$x$', fontsize=18)\n",
|
|||
|
|
"ax.set_ylabel(r'$f(x, \\beta)$', fontsize=18)\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Функция №3"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 487,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[1.36588575 0.48465322]\n",
|
|||
|
|
"3.7836263532723186e-05\n",
|
|||
|
|
"0.11229032607799314\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"beta = (1.37, 0.48)\n",
|
|||
|
|
"\n",
|
|||
|
|
"def f(x, b0, b1):\n",
|
|||
|
|
" return b0 + b1 * np.log(x)\n",
|
|||
|
|
"\n",
|
|||
|
|
"xdata = np.linspace(0.01,5,50)\n",
|
|||
|
|
"y = f(xdata, *beta)\n",
|
|||
|
|
"ydata = y + 0.05 * np.random.randn(len(xdata))\n",
|
|||
|
|
"\n",
|
|||
|
|
"from scipy.optimize import curve_fit\n",
|
|||
|
|
"beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
|
|||
|
|
"print(beta_opt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"lin_dev = sum(beta_cov[0])\n",
|
|||
|
|
"print(lin_dev)\n",
|
|||
|
|
"\n",
|
|||
|
|
"residuals = ydata - f(xdata, *beta_opt)\n",
|
|||
|
|
"fres = sum(residuals**2)\n",
|
|||
|
|
"print(fres)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 488,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlUAAAG6CAYAAAAh/LN4AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy80BEi2AAAACXBIWXMAAA9hAAAPYQGoP6dpAABWtElEQVR4nO3deXhU5d3G8e9MQjaSTEgmZIEAYd9kl13cQFDgldpaXFGrtK6VolXxteJa3Nr6Vq27olKq1oqIC4qgUjSyR0D2JBDIvk/2ZWbePyIDgeyZLcn9ua65OjlzzpzfJNq5fc5zfo/BbrfbEREREZE2MXq6ABEREZGOQKFKRERExAkUqkREREScQKFKRERExAkUqkREREScQKFKRERExAkUqkREREScwNfTBXRUNpuN9PR0QkJCMBgMni5HREREmsFut1NcXExsbCxGY8vGnhSqXCQ9PZ24uDhPlyEiIiKtcOzYMXr27NmiYxSqXCQkJASo/aOEhoZ6uBoRERFpDovFQlxcnON7vCUUqlzkxCW/0NBQhSoREZF2pjVTdzRRXURERMQJFKpEREREnEChSkRERMQJFKpEREREnEChSkRERMQJFKpEREREnEChSkRERMQJFKpEREREnEChSkRERMQJ1FFdRETEA6w2O1tS8skurqB7SADj48PxMba8i7d4D4UqERERN1u7J4OH1+wlo6jCsS3GFMDSuUOZNTzGg5W1L94WTBWqRERE3GjtngxuWbED+2nbM4squGXFDl68ZoyCVTN4YzDVnCoRERE3sdrsPLxm7xmBCnBse3jNXqy2+vboPKw2OwlJeaxOTCMhKe+M38eJYHpqoIKTwXTtngx3luugkSoRERE32ZKSf0YQOJUdyCiqYEtKPpP6RbivsHp46tJaUyNQTQVTA7XBdMbQ6BbXa7XZ2ZKc3+raFapERETcJLu44UDVmv1cxVOX1ppzadQU6Oe0YFpSAmlptY/Pv8vjk6+OU5ZW3Or6FapERETcpHtIgFP3cwVXzflqauSruSNQ98wa3OS57HZITqskuAyOH4fjyZUc31dS+7/HIS27C8cLulJUFXTKURE/Pywt/mwnKFSJiIi4yfj4cGJMAWQWVdQbHgxAtKk2cHhCay6tNecyYXNGvpp7aTSvuBJrhS9WSyA1xYH45hvxzwNjkS81xQGUl4VgqezGNU8FnnK0/88P11KoEhERcRMfo4Glc4dyy4odGKBOeDkRQ5bOHeqxtgAtnfPVnLDU3JGvE5c8bZU+1BQHYrUE4pNvJCAfjAU+1BQHUV4Wwp3PhFNm7dumzxlAOT1IoyfH6UEa4V1yCQqw4B9cSlVQMU8mte59DXa7vXPfYuAiFosFk8lEUVERoaGhni5HRES8iDe2AwBYnZjGne8mNrnf/10xCn9fY71h6UQcfPGaMcwYGs3UJzc4PqfdaqCmOACrJRBDgS+BuXaCSvzo1SWClAxfUvNDKLMFt+kzdKWEOI7Rk+P0NKbTM9RCT3MlPWNtxMX70mNgV8IHRGDo2QN69uTjTCu//89PjuNtlWUce/bXrfr+1kiViIiIm80aHsOModFe1bgSmj+Xy9zVn7s/+LFOoLLbwVbRBaslEFuhP3/8QwZjA8vJ2W7GVhKMpTwMS3U37PV0c/rpjC31C6KUOI4RxzF6GDMw+ecTGFiEb0g5dlM1/j18uWTWEMZNHQE9R4L5QjA23j0qsiqvmWdvmkKViIiIB/gYDU5tm+CMFgiNzfmy2wzYSvwJrQlj3b/t5HwYjH9+GNWWQMrKTBRWhFNpPzmPKQvY04Jzd6HKEZhiDWmE+efRNdCCb0gZhNVQFWHnysvOqg1McWMgPByrnWZ95sZ+N03Nc2sJhSoREZF2zhmXEysr4dgxA/9jHsnLXx3GPwco8KOyOJiSchMFVRHYfo4NDwMQ2aIao8mgF6n05DjhfjmEBBbiF1wKpioum9WTcVPiMPaOY32pmQc21ZBhCTvjs4w77bP4GGgymDb1uzl9nltbaE6Vi2hOlYiIuENDE8FPnds0a3gMFRWQmgpHkqwc2WXhyJ4SjiRZOZrmw5HcYDLKTPVemmuOQMroRSq9OUqUTwamgAICuhYzfkQge6oKyQ6xkxUWTnpoJNnB3bAZfRw1RpsC2HTvBWe0V3DGpdHm/m5O7Pvwmr2kZee3ek6VQpWLKFSJiDifty2g62lWm90xEdxuNVBjCcRWEEBgth2/XAMU+FNdGkJFtZn0sm6tPk84efTmKL0NqfQOzicuspx8ey7VwZVUmO0URASSbupOemgk5X4BdcLSur2Z3LJiB1D/3Y6uWuvw1N9NfeoLdFabna93HWXG6HhNVBcREe/izBDkrXfMuYvNBunpkJJsJyWxiJRdxfy4q4ysgz0oKQsnv9rc6pGmKDLpwxF6+xynT1ghvaMq6NMbeg/0p/cIE8GDekDv3hAzEnxqR5lOjAJB460hZg2P4cVrxpzxt4t28d+uNUsC+RgNjO/b+h5hClUiIuISzgxBruryDd41+mWxQHIyJO8uJWVnIcn7KkhOMZKcGcQRSzhV9i7Uxpawnx/NE00GfThCD+Nxuvnn0DW4CB9TBTURNZR19yGrWzh33jidC8/5JRia99lbEpY8cbejJ5YEUqgSERGnc2YIcuUCuu4e/bJaa9eZSzpQQ/K2fJJ+LCH5sI3kNH+S803kVZ243NT150fzRJBLPCn0NKYS7p9LUHARvqYyaiJslEYZ+f1vzuWP2y1sqwoCep9xvAF44Lsszps6DJ8W/ApbEpacfbdjUzyxJJBClYiIOJWzQ1BrLuM0h6tGv8rLISUFkn4sIWlbAUl7K0hKMZKc2ZUUSzhVdj9qv367//xoWhClxJNCL8NRugdk0zemgpGDjPQe7M/bx9M5GNSV1LBodvp3BUNPoCdwct5Q6bCzOJSwucH3b+3vENwflprLE0sCdfhQtWzZMj788EP2799PYGAgkydP5sknn2TQoEGNHvfvf/+bP/3pTxw5coQBAwbw5JNPcskll7ipahGR9svZIcgVl3HaGvyKiyHpsJ3D2wprH/uqSUr15XC2iePlJz5T8M+Pphmw0ZPj9CWZvl2z6RtZjMlczsHqPMqjIC+yK8fDotnbNYx9hu58S+0E71HDY8jck8Gqn+c21X3PWkvnDiW3pLJZdTjzUpineWJJoA4fqr799ltuu+02zj77bGpqarj//vu56KKL2Lt3L1271j+0+v3333PllVeybNky5syZw8qVK5k3bx47duxg+PDhbv4EIiLti7NDkCsu4zQn+KVl1/D26kICj9dweIeFQ/trOJzqz+G8MLIrw6j9au7286NpgZTRjyT6+h6jX3g+/WIr6NvfSN/hQfQZZ8Z/cDz0mgJdujR659rpoa85c5sSkprXNdyZl8K8gbsnyXe6lgo5OTl0796db7/9lmnTptW7z/z58yktLeWTTz5xbJs4cSKjRo3ipZdeatZ51FJBRDqrhKQ8rnz1hyb3+9fCic0aqToRMJq6jHN6r6PGnFjjzlbpgzU/kOA0KwFZRux5AZRZTORWRFFkbflloQhy6c9h+gVl0L+7hb69rPQb3IV+o0OJHtsDQ7++EN70+7bmd9jYhHtX/A7bk5bcjNCW7+8OP1J1uqKiIgDCG/mHOiEhgcWLF9fZNnPmTD766KMGj6msrKSy8uTwqsViaVuhIiLtlLPnsrT1Mk5lZe2luoMJeRzaWsjBvdXsOexLcc548q0t6woOEEsa/QzJ9A/Jpn90Cf3ibfQfHkC/s8MJG9kb4keD/8QWv++pWjPa19jcJk9cCvMm7pr31alClc1mY9GiRUyZMqXRy3iZmZlERUXV2RYVFUVmZmaDxyxbtoyHH37YabWKiLRXrfkCb2okoanLOBcNjeHYMTiw1cKB7/M4uKucA0m+HMwycbTUjA0fwPzzo2mxpNGXJAaG5TAwtoT+/Q30Gx5ATR9/8ntEE9J/EOP7T3VZCHHFJU9P9YvqTDpVqLrtttvYs2cPmzZtcvp7L1mypM7olsViIS4uzunnERHxBm0NQad+gTe3rcGs4TFM6hXNqi9yOLgpm6J
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"fig, ax = plt.subplots()\n",
|
|||
|
|
"ax.scatter(xdata, ydata)\n",
|
|||
|
|
"ax.plot(xdata, y, 'r', lw=2)\n",
|
|||
|
|
"ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
|
|||
|
|
"ax.set_xlim(0,5)\n",
|
|||
|
|
"ax.set_xlabel(r'$x$', fontsize=18)\n",
|
|||
|
|
"ax.set_ylabel(r'$f(x, \\beta)$', fontsize=18)\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Функция №4"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 489,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[0.8817479 1.92063655]\n",
|
|||
|
|
"0.00010562358913983954\n",
|
|||
|
|
"0.14631327681648387\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"beta = (0.89, 1.92)\n",
|
|||
|
|
"def f(x, b0, b1):\n",
|
|||
|
|
" return b0 + np.float_power(x, b1)\n",
|
|||
|
|
"\n",
|
|||
|
|
"xdata = np.linspace(0,5,50)\n",
|
|||
|
|
"y = f(xdata, *beta)\n",
|
|||
|
|
"ydata = y + 0.05 * np.random.randn(len(xdata))\n",
|
|||
|
|
"\n",
|
|||
|
|
"from scipy.optimize import curve_fit\n",
|
|||
|
|
"beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
|
|||
|
|
"print(beta_opt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"lin_dev = sum(beta_cov[0])\n",
|
|||
|
|
"print(lin_dev)\n",
|
|||
|
|
"\n",
|
|||
|
|
"residuals = ydata - f(xdata, *beta_opt)\n",
|
|||
|
|
"fres = sum(residuals**2)\n",
|
|||
|
|
"print(fres)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 490,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"fig, ax = plt.subplots()\n",
|
|||
|
|
"ax.scatter(xdata, ydata)\n",
|
|||
|
|
"ax.plot(xdata, y, 'r', lw=2)\n",
|
|||
|
|
"ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
|
|||
|
|
"ax.set_xlim(0,5)\n",
|
|||
|
|
"ax.set_xlabel(r'$x$', fontsize=18)\n",
|
|||
|
|
"ax.set_ylabel(r'$f(x, \\beta)$', fontsize=18)\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### 1.2.1 Задание\n",
|
|||
|
|
"\n",
|
|||
|
|
"Постройте модель линейной регрессии для произвольных данных из двух \n",
|
|||
|
|
"столбцов. Для примера можно взять точечную зависимость заработной платы от \n",
|
|||
|
|
"опыта работы: \n",
|
|||
|
|
"(https://raw.githubusercontent.com/AnnaShestova/salary-years-simple-linear-regression/master/Salary_Data.csv). \n",
|
|||
|
|
"Найдите коэффициенты линии регрессии. Постройте прогноз. "
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 491,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/html": [
|
|||
|
|
"<div>\n",
|
|||
|
|
"<style scoped>\n",
|
|||
|
|
" .dataframe tbody tr th:only-of-type {\n",
|
|||
|
|
" vertical-align: middle;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe tbody tr th {\n",
|
|||
|
|
" vertical-align: top;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe thead th {\n",
|
|||
|
|
" text-align: right;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"</style>\n",
|
|||
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|||
|
|
" <thead>\n",
|
|||
|
|
" <tr style=\"text-align: right;\">\n",
|
|||
|
|
" <th></th>\n",
|
|||
|
|
" <th>YearsExperience</th>\n",
|
|||
|
|
" <th>Salary</th>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </thead>\n",
|
|||
|
|
" <tbody>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>count</th>\n",
|
|||
|
|
" <td>30.000000</td>\n",
|
|||
|
|
" <td>30.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>mean</th>\n",
|
|||
|
|
" <td>5.313333</td>\n",
|
|||
|
|
" <td>76003.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>std</th>\n",
|
|||
|
|
" <td>2.837888</td>\n",
|
|||
|
|
" <td>27414.429785</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>min</th>\n",
|
|||
|
|
" <td>1.100000</td>\n",
|
|||
|
|
" <td>37731.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>25%</th>\n",
|
|||
|
|
" <td>3.200000</td>\n",
|
|||
|
|
" <td>56720.750000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>50%</th>\n",
|
|||
|
|
" <td>4.700000</td>\n",
|
|||
|
|
" <td>65237.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>75%</th>\n",
|
|||
|
|
" <td>7.700000</td>\n",
|
|||
|
|
" <td>100544.750000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>max</th>\n",
|
|||
|
|
" <td>10.500000</td>\n",
|
|||
|
|
" <td>122391.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </tbody>\n",
|
|||
|
|
"</table>\n",
|
|||
|
|
"</div>"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
" YearsExperience Salary\n",
|
|||
|
|
"count 30.000000 30.000000\n",
|
|||
|
|
"mean 5.313333 76003.000000\n",
|
|||
|
|
"std 2.837888 27414.429785\n",
|
|||
|
|
"min 1.100000 37731.000000\n",
|
|||
|
|
"25% 3.200000 56720.750000\n",
|
|||
|
|
"50% 4.700000 65237.000000\n",
|
|||
|
|
"75% 7.700000 100544.750000\n",
|
|||
|
|
"max 10.500000 122391.000000"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 491,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"url = 'https://raw.githubusercontent.com/AnnaShestova/salary-years-simple-linear-regression/master/Salary_Data.csv'\n",
|
|||
|
|
"\n",
|
|||
|
|
"ds = pd.read_csv(url)\n",
|
|||
|
|
"\n",
|
|||
|
|
"ds.describe()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 492,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"plt.scatter(ds['YearsExperience'], ds['Salary'])\n",
|
|||
|
|
"plt.xlabel('Опыт (годы)')\n",
|
|||
|
|
"plt.ylabel('Зарплата')\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 493,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"X = ds.iloc[:, :-1].values\n",
|
|||
|
|
"y = ds.iloc[:, 1].values\n",
|
|||
|
|
"\n",
|
|||
|
|
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 494,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"26780.099150628157\n",
|
|||
|
|
"[9312.57512673]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"regressor = LinearRegression()\n",
|
|||
|
|
"regressor.fit(X_train, y_train)\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(regressor.intercept_)\n",
|
|||
|
|
"print(regressor.coef_)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 495,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"y_pred = regressor.predict(X_test)\n",
|
|||
|
|
"df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 496,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"df.plot(kind='bar')\n",
|
|||
|
|
"plt.grid()\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 497,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"plt.scatter(X_test, y_test)\n",
|
|||
|
|
"plt.plot(X_test, y_pred, c='r')\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### 1.3.2 Задание\n",
|
|||
|
|
"\n",
|
|||
|
|
"Постройте модель множественной линейной регрессии для произвольных \n",
|
|||
|
|
"данных из нескольких столбцов. Для примера можно взять потребления \n",
|
|||
|
|
"газа (в миллионах галлонов) в 48 штатах США или набор данных о \n",
|
|||
|
|
"качестве красного вина (1) и (2) соответственно. Найдите коэффициенты \n",
|
|||
|
|
"множественной регрессии. Постройте прогноз. "
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 498,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/html": [
|
|||
|
|
"<div>\n",
|
|||
|
|
"<style scoped>\n",
|
|||
|
|
" .dataframe tbody tr th:only-of-type {\n",
|
|||
|
|
" vertical-align: middle;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe tbody tr th {\n",
|
|||
|
|
" vertical-align: top;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe thead th {\n",
|
|||
|
|
" text-align: right;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"</style>\n",
|
|||
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|||
|
|
" <thead>\n",
|
|||
|
|
" <tr style=\"text-align: right;\">\n",
|
|||
|
|
" <th></th>\n",
|
|||
|
|
" <th>fixed acidity</th>\n",
|
|||
|
|
" <th>volatile acidity</th>\n",
|
|||
|
|
" <th>citric acid</th>\n",
|
|||
|
|
" <th>residual sugar</th>\n",
|
|||
|
|
" <th>chlorides</th>\n",
|
|||
|
|
" <th>free sulfur dioxide</th>\n",
|
|||
|
|
" <th>total sulfur dioxide</th>\n",
|
|||
|
|
" <th>density</th>\n",
|
|||
|
|
" <th>pH</th>\n",
|
|||
|
|
" <th>sulphates</th>\n",
|
|||
|
|
" <th>alcohol</th>\n",
|
|||
|
|
" <th>quality</th>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </thead>\n",
|
|||
|
|
" <tbody>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>count</th>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" <td>1599.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>mean</th>\n",
|
|||
|
|
" <td>8.319637</td>\n",
|
|||
|
|
" <td>0.527821</td>\n",
|
|||
|
|
" <td>0.270976</td>\n",
|
|||
|
|
" <td>2.538806</td>\n",
|
|||
|
|
" <td>0.087467</td>\n",
|
|||
|
|
" <td>15.874922</td>\n",
|
|||
|
|
" <td>46.467792</td>\n",
|
|||
|
|
" <td>0.996747</td>\n",
|
|||
|
|
" <td>3.311113</td>\n",
|
|||
|
|
" <td>0.658149</td>\n",
|
|||
|
|
" <td>10.422983</td>\n",
|
|||
|
|
" <td>5.636023</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>std</th>\n",
|
|||
|
|
" <td>1.741096</td>\n",
|
|||
|
|
" <td>0.179060</td>\n",
|
|||
|
|
" <td>0.194801</td>\n",
|
|||
|
|
" <td>1.409928</td>\n",
|
|||
|
|
" <td>0.047065</td>\n",
|
|||
|
|
" <td>10.460157</td>\n",
|
|||
|
|
" <td>32.895324</td>\n",
|
|||
|
|
" <td>0.001887</td>\n",
|
|||
|
|
" <td>0.154386</td>\n",
|
|||
|
|
" <td>0.169507</td>\n",
|
|||
|
|
" <td>1.065668</td>\n",
|
|||
|
|
" <td>0.807569</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>min</th>\n",
|
|||
|
|
" <td>4.600000</td>\n",
|
|||
|
|
" <td>0.120000</td>\n",
|
|||
|
|
" <td>0.000000</td>\n",
|
|||
|
|
" <td>0.900000</td>\n",
|
|||
|
|
" <td>0.012000</td>\n",
|
|||
|
|
" <td>1.000000</td>\n",
|
|||
|
|
" <td>6.000000</td>\n",
|
|||
|
|
" <td>0.990070</td>\n",
|
|||
|
|
" <td>2.740000</td>\n",
|
|||
|
|
" <td>0.330000</td>\n",
|
|||
|
|
" <td>8.400000</td>\n",
|
|||
|
|
" <td>3.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>25%</th>\n",
|
|||
|
|
" <td>7.100000</td>\n",
|
|||
|
|
" <td>0.390000</td>\n",
|
|||
|
|
" <td>0.090000</td>\n",
|
|||
|
|
" <td>1.900000</td>\n",
|
|||
|
|
" <td>0.070000</td>\n",
|
|||
|
|
" <td>7.000000</td>\n",
|
|||
|
|
" <td>22.000000</td>\n",
|
|||
|
|
" <td>0.995600</td>\n",
|
|||
|
|
" <td>3.210000</td>\n",
|
|||
|
|
" <td>0.550000</td>\n",
|
|||
|
|
" <td>9.500000</td>\n",
|
|||
|
|
" <td>5.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>50%</th>\n",
|
|||
|
|
" <td>7.900000</td>\n",
|
|||
|
|
" <td>0.520000</td>\n",
|
|||
|
|
" <td>0.260000</td>\n",
|
|||
|
|
" <td>2.200000</td>\n",
|
|||
|
|
" <td>0.079000</td>\n",
|
|||
|
|
" <td>14.000000</td>\n",
|
|||
|
|
" <td>38.000000</td>\n",
|
|||
|
|
" <td>0.996750</td>\n",
|
|||
|
|
" <td>3.310000</td>\n",
|
|||
|
|
" <td>0.620000</td>\n",
|
|||
|
|
" <td>10.200000</td>\n",
|
|||
|
|
" <td>6.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>75%</th>\n",
|
|||
|
|
" <td>9.200000</td>\n",
|
|||
|
|
" <td>0.640000</td>\n",
|
|||
|
|
" <td>0.420000</td>\n",
|
|||
|
|
" <td>2.600000</td>\n",
|
|||
|
|
" <td>0.090000</td>\n",
|
|||
|
|
" <td>21.000000</td>\n",
|
|||
|
|
" <td>62.000000</td>\n",
|
|||
|
|
" <td>0.997835</td>\n",
|
|||
|
|
" <td>3.400000</td>\n",
|
|||
|
|
" <td>0.730000</td>\n",
|
|||
|
|
" <td>11.100000</td>\n",
|
|||
|
|
" <td>6.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>max</th>\n",
|
|||
|
|
" <td>15.900000</td>\n",
|
|||
|
|
" <td>1.580000</td>\n",
|
|||
|
|
" <td>1.000000</td>\n",
|
|||
|
|
" <td>15.500000</td>\n",
|
|||
|
|
" <td>0.611000</td>\n",
|
|||
|
|
" <td>72.000000</td>\n",
|
|||
|
|
" <td>289.000000</td>\n",
|
|||
|
|
" <td>1.003690</td>\n",
|
|||
|
|
" <td>4.010000</td>\n",
|
|||
|
|
" <td>2.000000</td>\n",
|
|||
|
|
" <td>14.900000</td>\n",
|
|||
|
|
" <td>8.000000</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </tbody>\n",
|
|||
|
|
"</table>\n",
|
|||
|
|
"</div>"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
" fixed acidity volatile acidity citric acid residual sugar \n",
|
|||
|
|
"count 1599.000000 1599.000000 1599.000000 1599.000000 \\\n",
|
|||
|
|
"mean 8.319637 0.527821 0.270976 2.538806 \n",
|
|||
|
|
"std 1.741096 0.179060 0.194801 1.409928 \n",
|
|||
|
|
"min 4.600000 0.120000 0.000000 0.900000 \n",
|
|||
|
|
"25% 7.100000 0.390000 0.090000 1.900000 \n",
|
|||
|
|
"50% 7.900000 0.520000 0.260000 2.200000 \n",
|
|||
|
|
"75% 9.200000 0.640000 0.420000 2.600000 \n",
|
|||
|
|
"max 15.900000 1.580000 1.000000 15.500000 \n",
|
|||
|
|
"\n",
|
|||
|
|
" chlorides free sulfur dioxide total sulfur dioxide density \n",
|
|||
|
|
"count 1599.000000 1599.000000 1599.000000 1599.000000 \\\n",
|
|||
|
|
"mean 0.087467 15.874922 46.467792 0.996747 \n",
|
|||
|
|
"std 0.047065 10.460157 32.895324 0.001887 \n",
|
|||
|
|
"min 0.012000 1.000000 6.000000 0.990070 \n",
|
|||
|
|
"25% 0.070000 7.000000 22.000000 0.995600 \n",
|
|||
|
|
"50% 0.079000 14.000000 38.000000 0.996750 \n",
|
|||
|
|
"75% 0.090000 21.000000 62.000000 0.997835 \n",
|
|||
|
|
"max 0.611000 72.000000 289.000000 1.003690 \n",
|
|||
|
|
"\n",
|
|||
|
|
" pH sulphates alcohol quality \n",
|
|||
|
|
"count 1599.000000 1599.000000 1599.000000 1599.000000 \n",
|
|||
|
|
"mean 3.311113 0.658149 10.422983 5.636023 \n",
|
|||
|
|
"std 0.154386 0.169507 1.065668 0.807569 \n",
|
|||
|
|
"min 2.740000 0.330000 8.400000 3.000000 \n",
|
|||
|
|
"25% 3.210000 0.550000 9.500000 5.000000 \n",
|
|||
|
|
"50% 3.310000 0.620000 10.200000 6.000000 \n",
|
|||
|
|
"75% 3.400000 0.730000 11.100000 6.000000 \n",
|
|||
|
|
"max 4.010000 2.000000 14.900000 8.000000 "
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 498,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"url = 'https://raw.githubusercontent.com/aniruddhachoudhury/Red-Wine-Quality/master/winequality-red.csv'\n",
|
|||
|
|
"\n",
|
|||
|
|
"ds = pd.read_csv(url)\n",
|
|||
|
|
"\n",
|
|||
|
|
"ds.describe()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 499,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"X = ds[['fixed acidity', 'volatile acidity', 'citric acid', 'residual sugar', 'chlorides', 'free sulfur dioxide', 'total sulfur dioxide', 'density', 'pH', 'sulphates', 'alcohol']]\n",
|
|||
|
|
"y = ds['quality']\n",
|
|||
|
|
"\n",
|
|||
|
|
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 500,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"34.99871062872134\n",
|
|||
|
|
"[ 4.12835075e-02 -1.14952802e+00 -1.77927063e-01 2.78700036e-02\n",
|
|||
|
|
" -1.87340739e+00 2.68362616e-03 -2.77748370e-03 -3.15166657e+01\n",
|
|||
|
|
" -2.54486051e-01 9.24040106e-01 2.67797417e-01]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"regressor = LinearRegression()\n",
|
|||
|
|
"regressor.fit(X_train, y_train)\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(regressor.intercept_)\n",
|
|||
|
|
"print(regressor.coef_)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 501,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/html": [
|
|||
|
|
"<div>\n",
|
|||
|
|
"<style scoped>\n",
|
|||
|
|
" .dataframe tbody tr th:only-of-type {\n",
|
|||
|
|
" vertical-align: middle;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe tbody tr th {\n",
|
|||
|
|
" vertical-align: top;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe thead th {\n",
|
|||
|
|
" text-align: right;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"</style>\n",
|
|||
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|||
|
|
" <thead>\n",
|
|||
|
|
" <tr style=\"text-align: right;\">\n",
|
|||
|
|
" <th></th>\n",
|
|||
|
|
" <th>Coefficient</th>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </thead>\n",
|
|||
|
|
" <tbody>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>fixed acidity</th>\n",
|
|||
|
|
" <td>0.041284</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>volatile acidity</th>\n",
|
|||
|
|
" <td>-1.149528</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>citric acid</th>\n",
|
|||
|
|
" <td>-0.177927</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>residual sugar</th>\n",
|
|||
|
|
" <td>0.027870</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>chlorides</th>\n",
|
|||
|
|
" <td>-1.873407</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>free sulfur dioxide</th>\n",
|
|||
|
|
" <td>0.002684</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>total sulfur dioxide</th>\n",
|
|||
|
|
" <td>-0.002777</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>density</th>\n",
|
|||
|
|
" <td>-31.516666</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>pH</th>\n",
|
|||
|
|
" <td>-0.254486</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>sulphates</th>\n",
|
|||
|
|
" <td>0.924040</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>alcohol</th>\n",
|
|||
|
|
" <td>0.267797</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </tbody>\n",
|
|||
|
|
"</table>\n",
|
|||
|
|
"</div>"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
" Coefficient\n",
|
|||
|
|
"fixed acidity 0.041284\n",
|
|||
|
|
"volatile acidity -1.149528\n",
|
|||
|
|
"citric acid -0.177927\n",
|
|||
|
|
"residual sugar 0.027870\n",
|
|||
|
|
"chlorides -1.873407\n",
|
|||
|
|
"free sulfur dioxide 0.002684\n",
|
|||
|
|
"total sulfur dioxide -0.002777\n",
|
|||
|
|
"density -31.516666\n",
|
|||
|
|
"pH -0.254486\n",
|
|||
|
|
"sulphates 0.924040\n",
|
|||
|
|
"alcohol 0.267797"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 501,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"pd.DataFrame(regressor.coef_, X.columns, columns=['Coefficient'])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 502,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/html": [
|
|||
|
|
"<div>\n",
|
|||
|
|
"<style scoped>\n",
|
|||
|
|
" .dataframe tbody tr th:only-of-type {\n",
|
|||
|
|
" vertical-align: middle;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe tbody tr th {\n",
|
|||
|
|
" vertical-align: top;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" .dataframe thead th {\n",
|
|||
|
|
" text-align: right;\n",
|
|||
|
|
" }\n",
|
|||
|
|
"</style>\n",
|
|||
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|||
|
|
" <thead>\n",
|
|||
|
|
" <tr style=\"text-align: right;\">\n",
|
|||
|
|
" <th></th>\n",
|
|||
|
|
" <th>Actual</th>\n",
|
|||
|
|
" <th>Predicted</th>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </thead>\n",
|
|||
|
|
" <tbody>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>1109</th>\n",
|
|||
|
|
" <td>6</td>\n",
|
|||
|
|
" <td>5.782930</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>1032</th>\n",
|
|||
|
|
" <td>5</td>\n",
|
|||
|
|
" <td>5.036193</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>1002</th>\n",
|
|||
|
|
" <td>7</td>\n",
|
|||
|
|
" <td>6.596989</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>487</th>\n",
|
|||
|
|
" <td>6</td>\n",
|
|||
|
|
" <td>5.339126</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>979</th>\n",
|
|||
|
|
" <td>5</td>\n",
|
|||
|
|
" <td>5.939529</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>...</th>\n",
|
|||
|
|
" <td>...</td>\n",
|
|||
|
|
" <td>...</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>794</th>\n",
|
|||
|
|
" <td>6</td>\n",
|
|||
|
|
" <td>6.559757</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>813</th>\n",
|
|||
|
|
" <td>4</td>\n",
|
|||
|
|
" <td>6.017576</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>1322</th>\n",
|
|||
|
|
" <td>5</td>\n",
|
|||
|
|
" <td>6.251291</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>704</th>\n",
|
|||
|
|
" <td>4</td>\n",
|
|||
|
|
" <td>5.163926</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" <tr>\n",
|
|||
|
|
" <th>1023</th>\n",
|
|||
|
|
" <td>6</td>\n",
|
|||
|
|
" <td>6.367205</td>\n",
|
|||
|
|
" </tr>\n",
|
|||
|
|
" </tbody>\n",
|
|||
|
|
"</table>\n",
|
|||
|
|
"<p>320 rows × 2 columns</p>\n",
|
|||
|
|
"</div>"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
" Actual Predicted\n",
|
|||
|
|
"1109 6 5.782930\n",
|
|||
|
|
"1032 5 5.036193\n",
|
|||
|
|
"1002 7 6.596989\n",
|
|||
|
|
"487 6 5.339126\n",
|
|||
|
|
"979 5 5.939529\n",
|
|||
|
|
"... ... ...\n",
|
|||
|
|
"794 6 6.559757\n",
|
|||
|
|
"813 4 6.017576\n",
|
|||
|
|
"1322 5 6.251291\n",
|
|||
|
|
"704 4 5.163926\n",
|
|||
|
|
"1023 6 6.367205\n",
|
|||
|
|
"\n",
|
|||
|
|
"[320 rows x 2 columns]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 502,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"y_pred = regressor.predict(X_test)\n",
|
|||
|
|
"df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})\n",
|
|||
|
|
"\n",
|
|||
|
|
"df"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Средняя квадратичная ошибка"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 503,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"0.38447119782012573"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 503,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"metrics.mean_squared_error(y_test,y_pred)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### 1.3.2 Задание*\n",
|
|||
|
|
"\n",
|
|||
|
|
"Экспериментально получены N − значений величины Y при \n",
|
|||
|
|
"различных значениях величины X. Построить полиномы первой и второй \n",
|
|||
|
|
"степени, аппроксимирующие результаты эксперимента, с применением \n",
|
|||
|
|
"метода наименьших квадратов. Результаты выводятся в виде таблиц \n",
|
|||
|
|
"значений и графиков, полученных полиномов. \n",
|
|||
|
|
"\n",
|
|||
|
|
"*Вариант:* 2"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 504,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"# Линейная функция\n",
|
|||
|
|
"def linear_func(x, b0, b1):\n",
|
|||
|
|
" return b0 + b1 * x\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Квадратичная функция\n",
|
|||
|
|
"def quadratic_func(x, b0, b1, b2):\n",
|
|||
|
|
" return b0 + b1 * x + b2 * x**2"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 505,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"xdata = np.linspace(0, 1, 6)\n",
|
|||
|
|
"ydata = np.asarray([5.0, 5.0, 4.0, 4.0, 6.0, 6.0])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 506,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[4.42857143 1.14285715]\n",
|
|||
|
|
" x y\n",
|
|||
|
|
"0 0.0 4.428571\n",
|
|||
|
|
"1 0.2 4.657143\n",
|
|||
|
|
"2 0.4 4.885714\n",
|
|||
|
|
"3 0.6 5.114286\n",
|
|||
|
|
"4 0.8 5.342857\n",
|
|||
|
|
"5 1.0 5.571429\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"beta_opt, beta_cov = curve_fit(linear_func, xdata, ydata, method='lm')\n",
|
|||
|
|
"print(beta_opt)\n",
|
|||
|
|
"df = pd.DataFrame({\"x\": xdata, \"y\": linear_func(xdata, *beta_opt)});\n",
|
|||
|
|
"#df.columns=['xdata', 'ydata']\n",
|
|||
|
|
"print(df)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 507,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"fig, ax = plt.subplots()\n",
|
|||
|
|
"ax.scatter(xdata, ydata)\n",
|
|||
|
|
"ax.plot(xdata, linear_func(xdata, *beta_opt), 'b', lw=2)\n",
|
|||
|
|
"plt.xlabel('x')\n",
|
|||
|
|
"plt.ylabel('linear')\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 508,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[ 5.14285714 -4.2142857 5.35714285]\n",
|
|||
|
|
" x y\n",
|
|||
|
|
"0 0.0 5.142857\n",
|
|||
|
|
"1 0.2 4.514286\n",
|
|||
|
|
"2 0.4 4.314286\n",
|
|||
|
|
"3 0.6 4.542857\n",
|
|||
|
|
"4 0.8 5.200000\n",
|
|||
|
|
"5 1.0 6.285714\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"beta_opt, beta_cov = curve_fit(quadratic_func, xdata, ydata, method='lm')\n",
|
|||
|
|
"print(beta_opt)\n",
|
|||
|
|
"df = pd.DataFrame({\"x\": xdata, \"y\": quadratic_func(xdata, *beta_opt)});\n",
|
|||
|
|
"print(df)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 509,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"fig, ax = plt.subplots()\n",
|
|||
|
|
"ax.scatter(xdata, ydata)\n",
|
|||
|
|
"ax.plot(xdata, quadratic_func(xdata, *beta_opt), 'b', lw=2)\n",
|
|||
|
|
"plt.xlabel('x')\n",
|
|||
|
|
"plt.ylabel('linear')\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"metadata": {
|
|||
|
|
"kernelspec": {
|
|||
|
|
"display_name": "Python 3",
|
|||
|
|
"language": "python",
|
|||
|
|
"name": "python3"
|
|||
|
|
},
|
|||
|
|
"language_info": {
|
|||
|
|
"codemirror_mode": {
|
|||
|
|
"name": "ipython",
|
|||
|
|
"version": 3
|
|||
|
|
},
|
|||
|
|
"file_extension": ".py",
|
|||
|
|
"mimetype": "text/x-python",
|
|||
|
|
"name": "python",
|
|||
|
|
"nbconvert_exporter": "python",
|
|||
|
|
"pygments_lexer": "ipython3",
|
|||
|
|
"version": "3.11.0"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 2
|
|||
|
|
}
|