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"# Simple Linear Regression\n",
"\n",
"*By James Peret – 30/07/2017*\n",
"\n",
"> Linear regression is a prediction method that is more than 200 years old.\n",
"\n",
"In statistics, [linear regression](https://en.wikipedia.org/wiki/Linear_regression) is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression.\n",
"\n",
"[Simple linear regression](https://en.wikipedia.org/wiki/Simple_linear_regression) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variables. The adjective simple refers to the fact that the outcome variable is related to a single predictor.\n",
"\n",
"### Libraries\n",
"\n",
"We will be using [pandas](https://pandas.pydata.org) for handling data structures and [matplotlib](https://matplotlib.org/) for plotting graphs."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
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"outputs": [],
"source": [
"# imports\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# this allows images to appear directly in the notebook\n",
"from IPython.display import Image\n",
"from IPython.core.display import HTML \n",
"\n",
"# this allows plots to appear directly in the notebook\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Data\n",
"\n",
"In this notebook we will be using a dataset of housing prices from the city of São Paulo, Brazil. The data was scraped from the web using this [notebook](../data/housing-prices-sao-paulo.ipynb)."
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
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"\n",
"
\n",
" \n",
" \n",
" | \n",
" meters | \n",
" price | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 100.0 | \n",
" 1150.0 | \n",
"
\n",
" \n",
" | 1 | \n",
" 102.0 | \n",
" 760.0 | \n",
"
\n",
" \n",
" | 2 | \n",
" 63.0 | \n",
" 519.0 | \n",
"
\n",
" \n",
" | 3 | \n",
" 30.0 | \n",
" 278.2 | \n",
"
\n",
" \n",
" | 4 | \n",
" 55.0 | \n",
" 400.0 | \n",
"
\n",
" \n",
"
\n",
"