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notebook.tex
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notebook.tex
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% Default to the notebook output style
% Inherit from the specified cell style.
\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
% Nicer default font (+ math font) than Computer Modern for most use cases
\usepackage{mathpazo}
% Basic figure setup, for now with no caption control since it's done
% automatically by Pandoc (which extracts  syntax from Markdown).
\usepackage{graphicx}
% We will generate all images so they have a width \maxwidth. This means
% that they will get their normal width if they fit onto the page, but
% are scaled down if they would overflow the margins.
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
\else\Gin@nat@width\fi}
\makeatother
\let\Oldincludegraphics\includegraphics
% Set max figure width to be 80% of text width, for now hardcoded.
\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}}
% Ensure that by default, figures have no caption (until we provide a
% proper Figure object with a Caption API and a way to capture that
% in the conversion process - todo).
\usepackage{caption}
\DeclareCaptionLabelFormat{nolabel}{}
\captionsetup{labelformat=nolabel}
\usepackage{adjustbox} % Used to constrain images to a maximum size
\usepackage{xcolor} % Allow colors to be defined
\usepackage{enumerate} % Needed for markdown enumerations to work
\usepackage{geometry} % Used to adjust the document margins
\usepackage{amsmath} % Equations
\usepackage{amssymb} % Equations
\usepackage{textcomp} % defines textquotesingle
% Hack from http://tex.stackexchange.com/a/47451/13684:
\At
Document{%
\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
}
\usepackage{upquote} % Upright quotes for verbatim code
\usepackage{eurosym} % defines \euro
\usepackage[mathletters]{ucs} % Extended unicode (utf-8) support
\usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document
\usepackage{fancyvrb} % verbatim replacement that allows latex
\usepackage{grffile} % extends the file name processing of package graphics
% to support a larger range
% The hyperref package gives us a pdf with properly built
% internal navigation ('pdf bookmarks' for the table of contents,
% internal cross-reference links, web links for URLs, etc.)
\usepackage{hyperref}
\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
% normalem makes italics be italics, not underlines
% Colors for the hyperref package
\definecolor{urlcolor}{rgb}{0,.145,.698}
\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
\definecolor{citecolor}{rgb}{.12,.54,.11}
% ANSI colors
\definecolor{ansi-black}{HTML}{3E424D}
\definecolor{ansi-black-intense}{HTML}{282C36}
\definecolor{ansi-red}{HTML}{E75C58}
\definecolor{ansi-red-intense}{HTML}{B22B31}
\definecolor{ansi-green}{HTML}{00A250}
\definecolor{ansi-green-intense}{HTML}{007427}
\definecolor{ansi-yellow}{HTML}{DDB62B}
\definecolor{ansi-yellow-intense}{HTML}{B27D12}
\definecolor{ansi-blue}{HTML}{208FFB}
\definecolor{ansi-blue-intense}{HTML}{0065CA}
\definecolor{ansi-magenta}{HTML}{D160C4}
\definecolor{ansi-magenta-intense}{HTML}{A03196}
\definecolor{ansi-cyan}{HTML}{60C6C8}
\definecolor{ansi-cyan-intense}{HTML}{258F8F}
\definecolor{ansi-white}{HTML}{C5C1B4}
\definecolor{ansi-white-intense}{HTML}{A1A6B2}
% commands and environments needed by pandoc snippets
% extracted from the output of `pandoc -s`
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\newenvironment{Shaded}{}{}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
\newcommand{\RegionMarkerTok}[1]{{#1}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\NormalTok}[1]{{#1}}
% Additional commands for more recent versions of Pandoc
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
\newcommand{\ImportTok}[1]{{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
\newcommand{\BuiltInTok}[1]{{#1}}
\newcommand{\ExtensionTok}[1]{{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
% Define a nice break command that doesn't care if a line doesn't already
% exist.
\def\br{\hspace*{\fill} \\* }
% Math Jax compatability definitions
\def\gt{>}
\def\lt{<}
% Document parameters
\title{ML01-Reg-Simple-Linear-Regression-Co2-py-v1}
% Pygments definitions
\makeatletter
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\def\PY@toks#1+{\ifx\relax#1\empty\else%
\PY@tok{#1}\expandafter\PY@toks\fi}
\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
\PY@it{\PY@bf{\PY@ff{#1}}}}}}}
\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
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% for compatibility with earlier versions
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% Exact colors from NB
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% Prevent overflowing lines due to hard-to-break entities
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% Setup hyperref package
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breaklinks=true, % so long urls are correctly broken across lines
colorlinks=true,
urlcolor=urlcolor,
linkcolor=linkcolor,
citecolor=citecolor,
}
% Slightly bigger margins than the latex defaults
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\begin{document}
\maketitle
\#
Simple Linear Regression
\hypertarget{about-this-notebook}{%
\paragraph{About this Notebook}\label{about-this-notebook}}
In this notebook, we learn how to use scikit-learn to implement simple
linear regression. We download a dataset that is related to fuel
consumption and Carbon dioxide emission of cars. Then, we split our data
into training and test sets, create a model using training set, Evaluate
your model using test set, and finally use model to predict unknown
value
\hypertarget{importing-needed-packages}{%
\subsubsection{Importing Needed
packages}\label{importing-needed-packages}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}4}]:} \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt}
\PY{k+kn}{import} \PY{n+nn}{pandas} \PY{k}{as} \PY{n+nn}{pd}
\PY{k+kn}{import} \PY{n+nn}{pylab} \PY{k}{as} \PY{n+nn}{pl}
\PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np}
\PY{o}{\PYZpc{}}\PY{k}{matplotlib} inline
\end{Verbatim}
\hypertarget{downloading-data}{%
\subsubsection{Downloading Data}\label{downloading-data}}
To download the data, we will use !wget to download it from IBM Object
Storage.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}5}]:} \PY{o}{!}wget \PYZhy{}O \PY{l+s+s2}{\PYZdq{}./data/FuelConsumption.csv\PYZdq{}} https://s3\PYZhy{}api.us\PYZhy{}geo.objectstorage.softlayer.net/cf\PYZhy{}courses\PYZhy{}data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
--2019-05-04 17:05:34-- https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv
Resolving s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net){\ldots} 67.228.254.193
Connecting to s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)|67.228.254.193|:443{\ldots} connected.
HTTP request sent, awaiting response{\ldots} 200 OK
Length: 72629 (71K) [text/csv]
Saving to: ‘./data/FuelConsumption.csv’
./data/FuelConsumpt 100\%[===================>] 70.93K --.-KB/s in 0.04s
2019-05-04 17:05:34 (1.81 MB/s) - ‘./data/FuelConsumption.csv’ saved [72629/72629]
\end{Verbatim}
\textbf{Did you know?} When it comes to Machine Learning, you will
likely be working with large datasets. As a business, where can you host
your data? IBM is offering a unique opportunity for businesses, with 10
Tb of IBM Cloud Object Storage:
\href{http://cocl.us/ML0101EN-IBM-Offer-CC}{Sign up now for free}
\hypertarget{understanding-the-data}{%
\subsection{Understanding the Data}\label{understanding-the-data}}
\hypertarget{fuelconsumption.csv}{%
\subsubsection{\texorpdfstring{\texttt{FuelConsumption.csv}:}{FuelConsumption.csv:}}\label{fuelconsumption.csv}}
We have downloaded a fuel consumption dataset,
\textbf{\texttt{FuelConsumption.csv}}, which contains model-specific
fuel consumption ratings and estimated carbon dioxide emissions for new
light-duty vehicles for retail sale in Canada.
\href{http://open.canada.ca/data/en/dataset/98f1a129-f628-4ce4-b24d-6f16bf24dd64}{Dataset
source}
\begin{itemize}
\tightlist
\item
\textbf{MODELYEAR} e.g.~2014
\item
\textbf{MAKE} e.g.~Acura
\item
\textbf{MODEL} e.g.~ILX
\item
\textbf{VEHICLE CLASS} e.g.~SUV
\item
\textbf{ENGINE SIZE} e.g.~4.7
\item
\textbf{CYLINDERS} e.g 6
\item
\textbf{TRANSMISSION} e.g.~A6
\item
\textbf{FUEL CONSUMPTION in CITY(L/100 km)} e.g.~9.9
\item
\textbf{FUEL CONSUMPTION in HWY (L/100 km)} e.g.~8.9
\item
\textbf{FUEL CONSUMPTION COMB (L/100 km)} e.g.~9.2
\item
\textbf{CO2 EMISSIONS (g/km)} e.g.~182 --\textgreater{} low
--\textgreater{} 0
\end{itemize}
\hypertarget{reading-the-data-in}{%
\subsection{Reading the data in}\label{reading-the-data-in}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}6}]:} \PY{n}{df} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{./data/FuelConsumption.csv}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{} take a look at the dataset}
\PY{n}{df}\PY{o}{.}\PY{n}{head}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}6}]:} MODELYEAR MAKE MODEL VEHICLECLASS ENGINESIZE CYLINDERS \textbackslash{}
0 2014 ACURA ILX COMPACT 2.0 4
1 2014 ACURA ILX COMPACT 2.4 4
2 2014 ACURA ILX HYBRID COMPACT 1.5 4
3 2014 ACURA MDX 4WD SUV - SMALL 3.5 6
4 2014 ACURA RDX AWD SUV - SMALL 3.5 6
TRANSMISSION FUELTYPE FUELCONSUMPTION\_CITY FUELCONSUMPTION\_HWY \textbackslash{}
0 AS5 Z 9.9 6.7
1 M6 Z 11.2 7.7
2 AV7 Z 6.0 5.8
3 AS6 Z 12.7 9.1
4 AS6 Z 12.1 8.7
FUELCONSUMPTION\_COMB FUELCONSUMPTION\_COMB\_MPG CO2EMISSIONS
0 8.5 33 196
1 9.6 29 221
2 5.9 48 136
3 11.1 25 255
4 10.6 27 244
\end{Verbatim}
\hypertarget{data-exploration}{%
\subsubsection{Data Exploration}\label{data-exploration}}
Lets first have a descriptive exploration on our data.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}7}]:} \PY{c+c1}{\PYZsh{} summarize the data}
\PY{n}{df}\PY{o}{.}\PY{n}{describe}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}7}]:} MODELYEAR ENGINESIZE CYLINDERS FUELCONSUMPTION\_CITY \textbackslash{}
count 1067.0 1067.000000 1067.000000 1067.000000
mean 2014.0 3.346298 5.794752 13.296532
std 0.0 1.415895 1.797447 4.101253
min 2014.0 1.000000 3.000000 4.600000
25\% 2014.0 2.000000 4.000000 10.250000
50\% 2014.0 3.400000 6.000000 12.600000
75\% 2014.0 4.300000 8.000000 15.550000
max 2014.0 8.400000 12.000000 30.200000
FUELCONSUMPTION\_HWY FUELCONSUMPTION\_COMB FUELCONSUMPTION\_COMB\_MPG \textbackslash{}
count 1067.000000 1067.000000 1067.000000
mean 9.474602 11.580881 26.441425
std 2.794510 3.485595 7.468702
min 4.900000 4.700000 11.000000
25\% 7.500000 9.000000 21.000000
50\% 8.800000 10.900000 26.000000
75\% 10.850000 13.350000 31.000000
max 20.500000 25.800000 60.000000
CO2EMISSIONS
count 1067.000000
mean 256.228679
std 63.372304
min 108.000000
25\% 207.000000
50\% 251.000000
75\% 294.000000
max 488.000000
\end{Verbatim}
Lets select some features to explore more.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}8}]:} \PY{n}{cdf} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ENGINESIZE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{CYLINDERS}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{FUELCONSUMPTION\PYZus{}COMB}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{CO2EMISSIONS}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{]}
\PY{n}{cdf}\PY{o}{.}\PY{n}{head}\PY{p}{(}\PY{l+m+mi}{9}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}8}]:} ENGINESIZE CYLINDERS FUELCONSUMPTION\_COMB CO2EMISSIONS
0 2.0 4 8.5 196
1 2.4 4 9.6 221
2 1.5 4 5.9 136
3 3.5 6 11.1 255
4 3.5 6 10.6 244
5 3.5 6 10.0 230
6 3.5 6 10.1 232
7 3.7 6 11.1 255
8 3.7 6 11.6 267
\end{Verbatim}
we can plot each of these fearues:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}9}]:} \PY{n}{viz} \PY{o}{=} \PY{n}{cdf}\PY{p}{[}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{CYLINDERS}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ENGINESIZE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{CO2EMISSIONS}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{FUELCONSUMPTION\PYZus{}COMB}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{]}
\PY{n}{viz}\PY{o}{.}\PY{n}{hist}\PY{p}{(}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_14_0.png}
\end{center}
{ \hspace*{\fill} \\}
Now, lets plot each of these features vs the Emission, to see how linear
is their relation:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}10}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{cdf}\PY{o}{.}\PY{n}{FUELCONSUMPTION\PYZus{}COMB}\PY{p}{,} \PY{n}{cdf}\PY{o}{.}\PY{n}{CO2EMISSIONS}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{FUELCONSUMPTION\PYZus{}COMB}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Emission}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_16_0.png}
\end{center}
{ \hspace*{\fill} \\}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}11}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{cdf}\PY{o}{.}\PY{n}{ENGINESIZE}\PY{p}{,} \PY{n}{cdf}\PY{o}{.}\PY{n}{CO2EMISSIONS}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Engine size}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Emission}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_17_0.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{practice}{%
\subsection{Practice}\label{practice}}
plot \textbf{CYLINDER} vs the Emission, to see how linear is their
relation:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}12}]:} \PY{c+c1}{\PYZsh{} write your code here}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}13}]:} \PY{c+c1}{\PYZsh{} Double\PYZhy{}click \PYZus{}\PYZus{}here\PYZus{}\PYZus{} for the solution.}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{cdf}\PY{o}{.}\PY{n}{CYLINDERS}\PY{p}{,} \PY{n}{cdf}\PY{o}{.}\PY{n}{CO2EMISSIONS}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Cylinders}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Emission}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_20_0.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{creating-train-and-test-dataset}{%
\paragraph{Creating train and test
dataset}\label{creating-train-and-test-dataset}}
Train/Test Split involves splitting the dataset into training and
testing sets respectively, which are mutually exclusive. After which,
you train with the training set and test with the testing set. This will
provide a more accurate evaluation on out-of-sample accuracy because the
testing dataset is not part of the dataset that have been used to train
the data. It is more realistic for real world problems.
This means that we know the outcome of each data point in this dataset,
making it great to test with! And since this data has not been used to
train the model, the model has no knowledge of the outcome of these data
points. So, in essence, it is truly an out-of-sample testing.
Lets split our dataset into train and test sets, 80\% of the entire data
for training, and the 20\% for testing. We create a mask to select
random rows using \textbf{np.random.rand()} function:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}14}]:} \PY{n}{np}\PY{o}{.}\PY{n}{random}\PY{o}{.}\PY{n}{rand}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}14}]:} array([ 0.40822998, 0.54672013, 0.59269407, {\ldots}, 0.56986627,
0.70155421, 0.86429307])
\end{Verbatim}
\hypertarget{intereesting-way-to-split-data-in-training-and-testing.}{%
\subsubsection{intereesting way to split data in training and
testing.}\label{intereesting-way-to-split-data-in-training-and-testing.}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}15}]:} \PY{n}{msk} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{random}\PY{o}{.}\PY{n}{rand}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)} \PY{o}{\PYZlt{}} \PY{l+m+mf}{0.8}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}16}]:} \PY{n}{msk}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}16}]:} array([False, False, False, {\ldots}, True, True, True], dtype=bool)
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}17}]:} \PY{n}{train} \PY{o}{=} \PY{n}{cdf}\PY{p}{[}\PY{n}{msk}\PY{p}{]}
\PY{n}{test} \PY{o}{=} \PY{n}{cdf}\PY{p}{[}\PY{o}{\PYZti{}}\PY{n}{msk}\PY{p}{]}
\end{Verbatim}
\hypertarget{simple-regression-model}{%
\subsubsection{Simple Regression Model}\label{simple-regression-model}}
Linear Regression fits a linear model with coefficients B = (B1,
\ldots{}, Bn) to minimize the `residual sum of squares' between the
independent x in the dataset, and the dependent y by the linear
approximation.
\hypertarget{train-data-distribution}{%
\paragraph{Train data distribution}\label{train-data-distribution}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}18}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{train}\PY{o}{.}\PY{n}{ENGINESIZE}\PY{p}{,} \PY{n}{train}\PY{o}{.}\PY{n}{CO2EMISSIONS}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Engine size}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Emission}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_29_0.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{modeling}{%
\paragraph{Modeling}\label{modeling}}
Using sklearn package to model data.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}19}]:} \PY{k+kn}{from} \PY{n+nn}{sklearn} \PY{k}{import} \PY{n}{linear\PYZus{}model}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}20}]:} \PY{c+c1}{\PYZsh{} initialize thee modeel object }
\PY{n}{regr} \PY{o}{=} \PY{n}{linear\PYZus{}model}\PY{o}{.}\PY{n}{LinearRegression}\PY{p}{(}\PY{p}{)}
\PY{c+c1}{\PYZsh{} prepare input data as number arrays}
\PY{n}{train\PYZus{}x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{asanyarray}\PY{p}{(}\PY{n}{train}\PY{p}{[}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ENGINESIZE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{train\PYZus{}y} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{asanyarray}\PY{p}{(}\PY{n}{train}\PY{p}{[}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{CO2EMISSIONS}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{c+c1}{\PYZsh{} fit thee model, this is done inplace}
\PY{n}{regr}\PY{o}{.}\PY{n}{fit} \PY{p}{(}\PY{n}{train\PYZus{}x}\PY{p}{,} \PY{n}{train\PYZus{}y}\PY{p}{)}
\PY{c+c1}{\PYZsh{} get the coefficients}
\PY{n+nb}{print} \PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Coefficients: }\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{regr}\PY{o}{.}\PY{n}{coef\PYZus{}}\PY{p}{)}
\PY{n+nb}{print} \PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Intercept: }\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{n}{regr}\PY{o}{.}\PY{n}{intercept\PYZus{}}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Coefficients: [[ 38.36444348]]
Intercept: [ 127.61527093]
\end{Verbatim}
As mentioned before, \textbf{Coefficient} and \textbf{Intercept} in the
simple linear regression, are the parameters of the fit line. Given that
it is a simple linear regression, with only 2 parameters, and knowing
that the parameters are the intercept and slope of the line, sklearn can
estimate them directly from our data. Notice that all of the data must
be available to traverse and calculate the parameters.
\hypertarget{plot-outputs}{%
\paragraph{Plot outputs}\label{plot-outputs}}
we can plot the fit line over the data:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}21}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{train}\PY{o}{.}\PY{n}{ENGINESIZE}\PY{p}{,} \PY{n}{train}\PY{o}{.}\PY{n}{CO2EMISSIONS}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}21}]:} <matplotlib.collections.PathCollection at 0x7f500ca41940>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_36_1.png}
\end{center}
{ \hspace*{\fill} \\}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}22}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{train}\PY{o}{.}\PY{n}{ENGINESIZE}\PY{p}{,} \PY{n}{train}\PY{o}{.}\PY{n}{CO2EMISSIONS}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{train\PYZus{}x}\PY{p}{,} \PY{n}{regr}\PY{o}{.}\PY{n}{coef\PYZus{}}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{n}{train\PYZus{}x} \PY{o}{+} \PY{n}{regr}\PY{o}{.}\PY{n}{intercept\PYZus{}}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{\PYZhy{}r}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Engine size}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Emission}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}22}]:} Text(0,0.5,'Emission')
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_37_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{evaluation}{%
\paragraph{Evaluation}\label{evaluation}}
we compare the actual values and predicted values to calculate the
accuracy of a regression model. Evaluation metrics provide a key role in
the development of a model, as it provides insight to areas that require
improvement.
There are different model evaluation metrics, lets use MSE here to
calculate the accuracy of our model based on the test set: - Mean
absolute error: It is the mean of the absolute value of the errors. This
is the easiest of the metrics to understand since it's just average
error. - Mean Squared Error (MSE): Mean Squared Error (MSE) is the mean
of the squared error. It's more popular than Mean absolute error because
the focus is geared more towards large errors. This is due to the
squared term exponentially increasing larger errors in comparison to
smaller ones. - Root Mean Squared Error (RMSE). - R-squared is not
error, but is a popular metric for accuracy of your model. It represents
how close the data are to the fitted regression line. The higher the
R-squared, the better the model fits your data. Best possible score is
1.0 and it can be negative (because the model can be arbitrarily worse).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}23}]:} \PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{metrics} \PY{k}{import} \PY{n}{r2\PYZus{}score}
\PY{n}{test\PYZus{}x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{asanyarray}\PY{p}{(}\PY{n}{test}\PY{p}{[}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ENGINESIZE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{test\PYZus{}y} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{asanyarray}\PY{p}{(}\PY{n}{test}\PY{p}{[}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{CO2EMISSIONS}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{test\PYZus{}y\PYZus{}} \PY{o}{=} \PY{n}{regr}\PY{o}{.}\PY{n}{predict}\PY{p}{(}\PY{n}{test\PYZus{}x}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Mean absolute error: }\PY{l+s+si}{\PYZpc{}.2f}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{test\PYZus{}y\PYZus{}} \PY{o}{\PYZhy{}} \PY{n}{test\PYZus{}y}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Residual sum of squares (MSE): }\PY{l+s+si}{\PYZpc{}.2f}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{(}\PY{n}{test\PYZus{}y\PYZus{}} \PY{o}{\PYZhy{}} \PY{n}{test\PYZus{}y}\PY{p}{)} \PY{o}{*}\PY{o}{*} \PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{R2\PYZhy{}score: }\PY{l+s+si}{\PYZpc{}.2f}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{r2\PYZus{}score}\PY{p}{(}\PY{n}{test\PYZus{}y\PYZus{}} \PY{p}{,} \PY{n}{test\PYZus{}y}\PY{p}{)} \PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Mean absolute error: 24.54
Residual sum of squares (MSE): 1055.78
R2-score: 0.63
\end{Verbatim}
\hypertarget{want-to-learn-more}{%
\subsection{Want to learn more?}\label{want-to-learn-more}}
IBM SPSS Modeler is a comprehensive analytics platform that has many
machine learning algorithms. It has been designed to bring predictive
intelligence to decisions made by individuals, by groups, by systems --
by your enterprise as a whole. A free trial is available through this
course, available here: \href{http://cocl.us/ML0101EN-SPSSModeler}{SPSS
Modeler}.
Also, you can use Watson Studio to run these notebooks faster with
bigger datasets. Watson Studio is IBM's leading cloud solution for data
scientists, built by data scientists. With Jupyter notebooks, RStudio,
Apache Spark and popular libraries pre-packaged in the cloud, Watson
Studio enables data scientists to collaborate on their projects without
having to install anything. Join the fast-growing community of Watson
Studio users today with a free account at
\href{https://cocl.us/ML0101EN_DSX}{Watson Studio}
\hypertarget{thanks-for-completing-this-lesson}{%
\subsubsection{Thanks for completing this
lesson!}\label{thanks-for-completing-this-lesson}}
Notebook created by: Saeed Aghabozorgi
Copyright © 2018 \href{https://cocl.us/DX0108EN_CC}{Cognitive Class}.
This notebook and its source code are released under the terms of the
\href{https://bigdatauniversity.com/mit-license/}{MIT License}.
% Add a bibliography block to the postdoc
\end{document}