{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Multiple Regression from scratch"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Requirement already satisfied: plotly in /usr/local/lib/python3.6/dist-packages (4.5.0)\n",
"Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from plotly) (1.14.0)\n",
"Requirement already satisfied: retrying>=1.3.3 in /usr/local/lib/python3.6/dist-packages (from plotly) (1.3.3)\n"
]
}
],
"source": [
"!pip3 install plotly"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"from random import random\n",
"from typing import Union, List\n",
"from plotly import express as px\n",
"from plotly import graph_objects as go"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# The data set we're using (source: https://miabellaai.net/)\n",
"data = [\n",
" [1.15, 0.59, 4.18],\n",
" [-1.23, 1.65, -1],\n",
" [-4.77, 4.02, -1.77],\n",
" [0.57, 0.13, 6.06],\n",
" [3.29, 3.14, 2.43],\n",
" [2.22, 3.58, 4.49],\n",
" [-3.98, 1.15, -2.64],\n",
" [-0.98, 1.01, 1.87],\n",
" [-2.26, 1.09, 3.43],\n",
" [-0.96, 0.24, 1.03],\n",
" [-2.92, 1.62, 1.8],\n",
" [3.88, -1.13, 5.59],\n",
" [0.01, 2.66, 4.42],\n",
" [3.3, 1.04, 3.7],\n",
" [0.44, 0.14, 1.2],\n",
" [4.7, -0.73, 6.95],\n",
" [-0.05, 1.3, 0.93],\n",
" [3.74, -1.46, 3.97],\n",
" [-3.69, 2.85, -2.07],\n",
" [-4.39, 7.78, -2.8],\n",
" [2.95, -1.02, 2.7],\n",
" [1.19, -0.35, 4.24],\n",
" [3.83, -1.72, 3.25],\n",
" [-4.57, 2.72, -0.6],\n",
" [-2.07, 5.79, 0.4],\n",
" [-1.56, 1.34, -0.61],\n",
" [0.85, 0.07, 1.06],\n",
" [3.13, -0.98, 2.88],\n",
" [-2.22, 0.6, 1.53],\n",
" [-2.98, 2.43, 2.04],\n",
" [2.59, 4.8, 1.8],\n",
" [1.43, -0.91, 2.92],\n",
" [-3.48, 2.24, 2.44],\n",
" [2.69, 2.38, 7.48],\n",
" [0.42, 4.33, 4.32],\n",
" [1.75, -0.23, 3.57],\n",
" [-4.17, 2.25, -0.3],\n",
" [1.35, 0.13, 3.63],\n",
" [-3.68, 1.77, -1.43],\n",
" [-3.34, 4.32, 3.05],\n",
" [-0.79, 0.62, 1.33],\n",
" [4.56, -1.85, 3.36],\n",
" [-4.25, 6.17, 0.95],\n",
" [-2.96, 1.8, 4.44],\n",
" [3.36, -1.06, 2.76],\n",
" [1.13, 1.79, 4.03],\n",
" [0.07, 0.72, 3.46],\n",
" [3.94, 4.01, 7.62],\n",
" [-0.81, 6.04, 0.31],\n",
" [2.21, 4.37, 5.33],\n",
" [-3.11, 6.65, -0.5],\n",
" [3.88, -1.07, 7.86],\n",
" [0.82, -0.46, -0.07],\n",
" [4.27, -1.21, 3.77],\n",
" [-3.98, 8.22, -2.81],\n",
" [-0.54, 0.34, 2.92],\n",
" [-1.34, 2.23, 3.63],\n",
" [-4.96, 2.03, -2.55],\n",
" [3.2, -1.22, 3.18],\n",
" [-2.17, 5.18, 1.87],\n",
" [-4.13, 7.58, -1.77],\n",
" [2.82, 3.2, 7.1],\n",
" [-1.16, 1.14, 0.71],\n",
" [-4.22, 1.29, 1.58],\n",
" [-1.21, 0.9, 0.16],\n",
" [-2.53, 1.82, -1.66],\n",
" [-3.56, 5.63, -2.12],\n",
" [3.39, -0.33, 7.96],\n",
" [4.2, -0.8, 3.76],\n",
" [0.52, 2.22, 0.51],\n",
" [3.86, -0.22, 3.88],\n",
" [2.05, 5.4, 1.56],\n",
" [1.27, 3.06, 1.48],\n",
" [4.81, 0.65, 3.43],\n",
" [4.58, -0.91, 7.02],\n",
" [3.16, -0.23, 4.17],\n",
" [2.51, 0.19, 2.9],\n",
" [-4.09, 5.52, -2.09],\n",
" [2.61, -0.66, 1.98],\n",
" [4.86, 1.16, 5.41],\n",
" [4.24, 2.87, 5.67],\n",
" [-3.27, 3.01, 1.81],\n",
" [-2.43, 3.56, 4.22],\n",
" [1.34, 0.17, 3.5],\n",
" [-0.74, 1.17, 1.41],\n",
" [4.38, -2.08, 4.16],\n",
" [4.42, -0.21, 4.72],\n",
" [4.87, 2.71, 7.01],\n",
" [-1.69, 4.08, -0.38],\n",
" [0.34, 0.65, 1.18],\n",
" [1.4, 4.44, 0.79],\n",
" [4.28, 0.77, 7.04],\n",
" [1.36, 3.11, 0.87],\n",
" [0.42, 5.54, 2.76],\n",
" [0.61, 1.6, 2.93],\n",
" [-1.12, 2.63, 1.65],\n",
" [0.49, 2.54, -0.23],\n",
" [-3.19, 6.53, 2.05],\n",
" [-2.45, 4.7, 1.29],\n",
" [4.07, -1.54, 2.2]\n",
"]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# Turn the data into a list of x vectors (one for every pair of x items) and a vector containing all the y items\n",
"xs: List[List[float]] = []\n",
"ys: List[float] = []\n",
"\n",
"for item in data:\n",
" x1: float = item[0]\n",
" x2: float = item[1]\n",
" y: float = item[2]\n",
" xs.append([x1, x2])\n",
" ys.append(y)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# A convenience function which creates a scatter plot with an optional hyperplane\n",
"def plot(xs: List[List[float]], ys: List[float], ys_pred: Union[List[float], None] = None) -> None:\n",
" # Translate our `xs` and `ys` into data Plotly understands\n",
" x: List[float] = [item[0] for item in xs] # x1\n",
" y: List[float] = [item[1] for item in xs] # x2\n",
" z: List[float] = ys\n",
" fig = px.scatter_3d(x=x, y=y, z=z, labels={'x': 'x1', 'y': 'x2', 'z': 'y'})\n",
" # If present, add the hyperplane\n",
" if ys_pred:\n",
" fig.add_trace(\n",
" go.Scatter3d(\n",
" x=x, y=y, z=ys_pred, name='Guess', surfaceaxis=1\n",
" )\n",
" )\n",
" fig.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
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