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517 lines
52 KiB
Plaintext
517 lines
52 KiB
Plaintext
6 months ago
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "ae02d6c8",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from sklearn import linear_model"
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]
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},
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{
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"cell_type": "markdown",
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"id": "18cfa351",
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"metadata": {},
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"source": [
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"<img src='linear_regression.png' width=50%>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e7ac8c6d",
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"metadata": {},
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"source": [
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"$$最小化\\sum^n_{i=1}(d_i)^2$$"
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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": 2,
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"id": "6729b5ba",
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"metadata": {},
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"outputs": [],
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"source": [
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"df = pd.read_csv(\"housing_price.csv\")"
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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": 3,
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"id": "717fda9f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>area</th>\n",
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" <th>price</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>0</th>\n",
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" <td>86.45</td>\n",
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" <td>117.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1</th>\n",
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" <td>91.57</td>\n",
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" <td>98.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2</th>\n",
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" <td>85.52</td>\n",
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" <td>114.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>3</th>\n",
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" <td>103.60</td>\n",
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" <td>146.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>4</th>\n",
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" <td>105.25</td>\n",
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" <td>106.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>5</th>\n",
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" <td>99.00</td>\n",
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" <td>109.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>6</th>\n",
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" <td>87.95</td>\n",
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" <td>91.5</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" area price\n",
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"0 86.45 117.0\n",
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"1 91.57 98.0\n",
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"2 85.52 114.0\n",
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"3 103.60 146.0\n",
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"4 105.25 106.0\n",
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"5 99.00 109.0\n",
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"6 87.95 91.5"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"df"
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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": 6,
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"id": "8bae038f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.collections.PathCollection at 0x129771424c8>"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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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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|
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"%matplotlib inline\n",
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|
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"plt.xlabel(\"area\")\n",
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"plt.ylabel(\"price\")\n",
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|
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"plt.scatter(df.area, df.price, c='r')"
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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": 18,
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"id": "1dbdd68d",
|
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"metadata": {},
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"outputs": [
|
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{
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"data": {
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"text/plain": [
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"(7, 1)"
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]
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},
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"execution_count": 18,
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"metadata": {},
|
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"output_type": "execute_result"
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}
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],
|
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"source": [
|
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"df[[\"area\"]].shape"
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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": 30,
|
||
|
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"id": "c147b635",
|
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"metadata": {},
|
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"outputs": [
|
||
|
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{
|
||
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"data": {
|
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"text/plain": [
|
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|
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"LinearRegression()"
|
||
|
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]
|
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|
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},
|
||
|
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"execution_count": 30,
|
||
|
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"metadata": {},
|
||
|
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"output_type": "execute_result"
|
||
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}
|
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],
|
||
|
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"source": [
|
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|
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"model = linear_model.LinearRegression()\n",
|
||
|
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"model.fit(df[[\"area\"]].values, df.price.values)"
|
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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": 31,
|
||
|
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"id": "cd1a7008",
|
||
|
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"metadata": {},
|
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"outputs": [
|
||
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{
|
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"data": {
|
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"text/plain": [
|
||
|
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"(array([0.83809367]), 32.70161672527138)"
|
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]
|
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},
|
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"execution_count": 31,
|
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"metadata": {},
|
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"output_type": "execute_result"
|
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}
|
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],
|
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"source": [
|
||
|
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"model.coef_, model.intercept_"
|
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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": 34,
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"id": "d7e74d63",
|
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"metadata": {},
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"outputs": [
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{
|
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"data": {
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"text/plain": [
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"array([115.93269948])"
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]
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},
|
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"execution_count": 34,
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"metadata": {},
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"output_type": "execute_result"
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}
|
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],
|
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"source": [
|
||
|
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"model.predict(np.array([[99.31]]))"
|
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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": 35,
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"id": "4fffcc21",
|
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"metadata": {},
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"outputs": [
|
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{
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"data": {
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"text/plain": [
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"array([115.93269948])"
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]
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},
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"execution_count": 35,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"price = model.coef_ * 99.31 + model.intercept_\n",
|
||
|
|
"price"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "410fa831",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"画出这条预测线"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 38,
|
||
|
|
"id": "a5fe689e",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stderr",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"D:\\envs\\stark-lin\\lib\\site-packages\\numpy\\core\\shape_base.py:65: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
|
||
|
|
" ary = asanyarray(ary)\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"[<matplotlib.lines.Line2D at 0x12978a40ec8>]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 38,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
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"data": {
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||
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|
"<Figure size 640x480 with 1 Axes>"
|
||
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|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"%matplotlib inline\n",
|
||
|
|
"plt.xlabel(\"area\")\n",
|
||
|
|
"plt.ylabel(\"price\")\n",
|
||
|
|
"plt.scatter(df.area, df.price, c='r')\n",
|
||
|
|
"plt.plot([0, 111],[model.intercept_, model.predict(np.array([[111]]))])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 42,
|
||
|
|
"id": "f7253975",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"preds = pd.read_csv(\"predict.csv\")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 45,
|
||
|
|
"id": "a27fe359",
|
||
|
|
"metadata": {},
|
||
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"outputs": [
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||
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"data": {
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"text/html": [
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||
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"<div>\n",
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"<style scoped>\n",
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|
" .dataframe tbody tr th:only-of-type {\n",
|
||
|
|
" vertical-align: middle;\n",
|
||
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|
" }\n",
|
||
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|
"\n",
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|
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|
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|
" }\n",
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|
"\n",
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|
"</style>\n",
|
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|
||
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|
||
|
|
" <tr style=\"text-align: right;\">\n",
|
||
|
|
" <th></th>\n",
|
||
|
|
" <th>area</th>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" </thead>\n",
|
||
|
|
" <tbody>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>0</th>\n",
|
||
|
|
" <td>150</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>1</th>\n",
|
||
|
|
" <td>128</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>2</th>\n",
|
||
|
|
" <td>111</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>3</th>\n",
|
||
|
|
" <td>138</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" </tbody>\n",
|
||
|
|
"</table>\n",
|
||
|
|
"</div>"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" area\n",
|
||
|
|
"0 150\n",
|
||
|
|
"1 128\n",
|
||
|
|
"2 111\n",
|
||
|
|
"3 138"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 45,
|
||
|
|
"metadata": {},
|
||
|
|
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|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
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|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
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|
|
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|
||
|
|
"execution_count": 50,
|
||
|
|
"id": "a7ac643a",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"preds[\"predicted\"] = model.predict(preds[[\"area\"]].values)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 51,
|
||
|
|
"id": "bef47aea",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
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|
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|
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|
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|
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|
" }\n",
|
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|
|
"\n",
|
||
|
|
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|
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|
" }\n",
|
||
|
|
"\n",
|
||
|
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|
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|
|
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|
||
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|
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|
"</style>\n",
|
||
|
|
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|
||
|
|
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|
||
|
|
" <tr style=\"text-align: right;\">\n",
|
||
|
|
" <th></th>\n",
|
||
|
|
" <th>area</th>\n",
|
||
|
|
" <th>predicted</th>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" </thead>\n",
|
||
|
|
" <tbody>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>0</th>\n",
|
||
|
|
" <td>150</td>\n",
|
||
|
|
" <td>158.415668</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>1</th>\n",
|
||
|
|
" <td>128</td>\n",
|
||
|
|
" <td>139.977607</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>2</th>\n",
|
||
|
|
" <td>111</td>\n",
|
||
|
|
" <td>125.730015</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" <tr>\n",
|
||
|
|
" <th>3</th>\n",
|
||
|
|
" <td>138</td>\n",
|
||
|
|
" <td>148.358544</td>\n",
|
||
|
|
" </tr>\n",
|
||
|
|
" </tbody>\n",
|
||
|
|
"</table>\n",
|
||
|
|
"</div>"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" area predicted\n",
|
||
|
|
"0 150 158.415668\n",
|
||
|
|
"1 128 139.977607\n",
|
||
|
|
"2 111 125.730015\n",
|
||
|
|
"3 138 148.358544"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 51,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
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|
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|
||
|
|
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|
||
|
|
"preds"
|
||
|
|
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|
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|
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|
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{
|
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|
|
"cell_type": "code",
|
||
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|
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|
||
|
|
"id": "e29158e1",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3 (ipykernel)",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
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||
|
|
"language_info": {
|
||
|
|
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|
||
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|
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|
||
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|
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|
||
|
|
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|
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|
|
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|
||
|
|
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|
||
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|
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|
||
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|
||
|
|
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|
||
|
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|
||
|
|
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|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|