383 lines
36 KiB
Plaintext
383 lines
36 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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"id": "specialized-stanley",
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"metadata": {},
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"source": [
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"# Ungraded Lab: Model Representation\n",
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"\n",
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"In this ungraded lab, you will implement the model $f$ for linear regression with one variable.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "active-bernard",
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"metadata": {},
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"source": [
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"## Problem Statement\n",
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"\n",
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"You will use the motivating example of housing price prediction again. For sake of simplicity, let's assume that you just have two data points - a house with 1000 square feet sold for \\\\$200,000 and a house with 2000 square feet sold for \\\\$400,000.\n",
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"\n",
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"Therefore, your dataset contains the following two points - \n",
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"\n",
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"| Size (feet$^2$) | Price (1000s of dollars) |\n",
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"| -------------------| ------------------------ |\n",
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"| 1000 | 200 |\n",
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"| 2000 | 400 |\n",
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"\n",
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"You'd like to fit a linear regression model (represented with a straight line) through these two points, so you can then predict price for other houses - say, a house with 1200 feet$^2$.\n",
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"\n",
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"### Notation: `X` and `y`\n",
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"\n",
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"For the next few labs, you will use lists in python to represent your dataset. As shown in the video:\n",
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"- `X` represents input variables, also called input features (in this case - Size (feet$^2$)) and \n",
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"- `y` represents output variables, also known as target variables (in this case - Price (1000s of dollars)). \n",
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"\n",
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"Please run the following code cell to create your `X` and `y` variables."
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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": 10,
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"id": "headed-custom",
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"metadata": {},
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"outputs": [],
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"source": [
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"# X is the input variable (size in square feet)\n",
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"# y in the output variable (price in 1000s of dollars)\n",
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"X = [1000, 2000] \n",
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"y = [200, 400]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "dependent-attribute",
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"metadata": {},
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"source": [
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"### Number of training examples `m`\n",
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"You will use `m` to denote the number of training examples. In Python, use the `len()` function to get the number of examples in a list. You can get `m` by running the next code cell."
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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": 11,
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"id": "novel-vessel",
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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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"Number of training examples is: 2\n"
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]
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}
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],
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"source": [
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"# m is the number of training examples\n",
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"m = len(X)\n",
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"print(\"Number of training examples is: %d\" %m)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "permanent-uncertainty",
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"metadata": {},
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"source": [
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"### Training example `x_i, y_i`\n",
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"\n",
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"You will use (x$^i$, y$^i$) to denote the $i^{th}$ training example. Since Python is zero indexed, (x$^0$, y$^0$) is (1000, 200) and (x$^1$, y$^1$) is (2000, 300). \n",
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"\n",
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"Run the next code block below to get the $i^{th}$ training example in a Python list."
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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": 12,
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"id": "executive-chick",
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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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"(x^(0), y^(0)) = (1000, 200)\n"
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]
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}
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],
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"source": [
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"i = 0 # Change this to 1 to see (x^1, y^1)\n",
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"\n",
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"x_i = X[i]\n",
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"y_i = y[i]\n",
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"print(\"(x^(%d), y^(%d)) = (%d, %d)\" %(i, i, x_i, y_i))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "solid-sharing",
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"metadata": {},
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"source": [
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"### Plotting the data\n",
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"First, let's run the cell below to import [matplotlib](http://matplotlib.org), which is a famous library to plot graphs in Python. "
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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": 13,
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"id": "designing-sociology",
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"id": "virgin-germany",
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"metadata": {},
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"source": [
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"You can plot these two points using the `scatter()` function in the `matplotlib` library, as shown in the cell below. \n",
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"- The function arguments `marker` and `c` show the points as red crosses (the default is blue dots).\n",
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"\n",
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"You can also use other functions in the `matplotlib` library to display the title and labels for the axes."
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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": 14,
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"id": "reduced-cartoon",
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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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"Text(0.5, 0, 'Size (feet^2)')"
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]
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},
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"execution_count": 14,
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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 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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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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"# Plot the data points\n",
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"plt.scatter(X, y, marker='x', c='r')\n",
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"\n",
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"# Set the title\n",
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"plt.title(\"Housing Prices\")\n",
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"# Set the y-axis label\n",
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"plt.ylabel('Price (in 1000s of dollars)')\n",
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"# Set the x-axis label\n",
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"plt.xlabel('Size (feet^2)')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "level-nirvana",
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"metadata": {},
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"source": [
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"## Model function\n",
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"\n",
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"The model function for linear regression (which is a function that maps from `X` to `y`) is represented as \n",
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"\n",
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"$f(x) = w_0 + w_1x$\n",
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"\n",
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"The formula above is how you can represent straight lines - different values of $w_0$ and $w_1$ give you different straight lines on the plot. Let's try to get a better intuition for this through the code blocks below.\n",
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"\n",
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"Let's represent $w$ as a list in python, with $w_0$ as the first item in the list and $w_1$ as the second. \n",
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"\n",
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"Let's start with $w_0 = 3$ and $w_1 = 1$ \n",
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"\n",
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"### Note: You can come back to this cell to adjust the model's w0 and w1 parameters"
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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": 29,
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"id": "temporal-investor",
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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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"w_0: 1\n",
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"w_1: 0.2\n"
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]
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}
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],
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"source": [
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"# You can come back here later to adjust w0 and w1\n",
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"w = [1, 0.2] \n",
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"print(\"w_0:\", w[0])\n",
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"print(\"w_1:\", w[1])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "capable-westminster",
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"metadata": {},
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"source": [
|
||
|
|
"Now, let's calculate the value of $f(x)$ for your two data points. You can explicitly write this out for each data point as - \n",
|
||
|
|
"\n",
|
||
|
|
"for $x^0$, `f = w[0]+w[1]*X[0]`\n",
|
||
|
|
"\n",
|
||
|
|
"for $x^1$, `f = w[0]+w[1]*X[1]`\n",
|
||
|
|
"\n",
|
||
|
|
"For a large number of data points, this can get unwieldy and repetitive. So instead, you can calculate the function output in a `for` loop as follows - \n",
|
||
|
|
"\n",
|
||
|
|
"```\n",
|
||
|
|
"f = []\n",
|
||
|
|
"for i in range(len(X)):\n",
|
||
|
|
" f_x = w[0] + w[1]*X[i]\n",
|
||
|
|
" f.append(f_x)\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"Paste the code shown above in the `calculate_hypothesis` function below."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 30,
|
||
|
|
"id": "tracked-bubble",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def calculate_model_output(w, X):\n",
|
||
|
|
" # Copy the code shown in the markdown here\n",
|
||
|
|
" f = []\n",
|
||
|
|
" for i in range(len(X)):\n",
|
||
|
|
" f_x = w[0] + w[1]*X[i]\n",
|
||
|
|
" f.append(f_x)\n",
|
||
|
|
" return f"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "blind-vocabulary",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Now let's call the `calculate_hypothesis` function and plot the output using the `plot` method from `matplotlib` libarary."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 31,
|
||
|
|
"id": "blocked-franklin",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"Text(0.5, 0, 'Size (feet^2)')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 31,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"f = calculate_model_output(w, X)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot our hypothesis\n",
|
||
|
|
"plt.plot(X, f, c='b')\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot the data points\n",
|
||
|
|
"plt.scatter(X, y, marker='x', c='r')\n",
|
||
|
|
"\n",
|
||
|
|
"# Set the title\n",
|
||
|
|
"plt.title(\"Housing Prices\")\n",
|
||
|
|
"# Set the y-axis label\n",
|
||
|
|
"plt.ylabel('Price (in 1000s of dollars)')\n",
|
||
|
|
"# Set the x-axis label\n",
|
||
|
|
"plt.xlabel('Size (feet^2)')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "dominican-panel",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"As you can see, $w_0 = 2$ and $w_1 = 1$ does not result in a line that fits our data. \n",
|
||
|
|
"\n",
|
||
|
|
"### Challenge\n",
|
||
|
|
"Try experimenting with different values of $w_0$ and $w_1$. What should the values be for getting a line that fits our data?\n",
|
||
|
|
"\n",
|
||
|
|
"#### Tip:\n",
|
||
|
|
"You can use your mouse to click on the triangle to the left of the green \"Hints\" below to reveal some hints for choosing w0 and w1."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "respected-median",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"<details>\n",
|
||
|
|
"<summary>\n",
|
||
|
|
" <font size='3', color='darkgreen'><b>Hints</b></font>\n",
|
||
|
|
"</summary>\n",
|
||
|
|
" <p>\n",
|
||
|
|
" <ul>\n",
|
||
|
|
" <li>Try w0 = 1 and w1 = 0.5, or w = [0, 0.2] </li>\n",
|
||
|
|
" </ul>\n",
|
||
|
|
" </p>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"id": "recreational-tennis",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"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": "3.9.1"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|