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% Document Info
\author{isantabarbara (isantabarbara)}
\pdfinfo{
  /Title (regression.pdf)
  /Creator (Cheatography)
  /Author (isantabarbara (isantabarbara))
  /Subject (Regression Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Regression Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{isantabarbara (isantabarbara)} via \textcolor{DarkBackground}{\uline{cheatography.com/55251/cs/14706/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}isantabarbara (isantabarbara) \\
  \uline{cheatography.com/isantabarbara} \\
        \uline{\seqsplit{www}.google.com}
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 6th April, 2018.\\
   Page {\thepage} of \pageref{LastPage}.
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\end{multicols}}




\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{What is Regression Analysis?}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{A form of {\bf{predictive modelling technique}} which investigates the relationship between a dependent ({\emph{target}}) and independent variable(s) ({\emph{predictor}})} \tn 
% Row Count 4 (+ 4)
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\mymulticolumn{1}{x{5.377cm}}{1.  Shows {\bf{significant relationships}} btw. target and predictors} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{2. Shows {\bf{strength of impact}} of multiple predictor on a target} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Coefficients}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Mean change in the response variable for {\bf{one unit of change}} in the predictor variable while holding other predictors in the model constant.} \tn 
% Row Count 3 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}Think of them as slopes}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Polynomial Regression (y=a+b*x\textasciicircum{}2...)}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Curve that fits} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Higher degree polynomial -\textgreater{} over-fitting risk} \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Polynomial Regression}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/isantabarbara_1518610777_underfitting-overfitting[1].png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Multicollinearity}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Multicollinearity test: Variance inflation factors (VIF \textgreater{}= 5)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Increase the variance of the coeff. estimates (makes them sensitive)} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Stepwise regression does not work as well} \tn 
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\mymulticolumn{1}{x{5.377cm}}{Doesn't affect the overall fit of the model} \tn 
% Row Count 6 (+ 1)
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\mymulticolumn{1}{x{5.377cm}}{Doesn't produce bad predictions} \tn 
% Row Count 7 (+ 1)
% Row 5
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\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{SOLUTIONS}}} \tn 
% Row Count 8 (+ 1)
% Row 6
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\mymulticolumn{1}{x{5.377cm}}{- Standardized predictors} \tn 
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% Row 7
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\mymulticolumn{1}{x{5.377cm}}{- Removing highly correlated predictors} \tn 
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% Row 8
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\mymulticolumn{1}{x{5.377cm}}{- Linearly combining predictors (x.e. sum)} \tn 
% Row Count 11 (+ 1)
% Row 9
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\mymulticolumn{1}{x{5.377cm}}{- Different analyses: PLS or PCA} \tn 
% Row Count 12 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Stepwise Regression}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Maximize prediction power with minimum number of predictor variables} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Fits the regression model by adding/dropping co-variates one at a time} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{- {\bf{Standard stepwise regression}} adds and removes predictors as needed for each step.} \tn 
% Row Count 6 (+ 2)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{- {\bf{Forward selection}} starts with most significant predictor and adds variable for each step.} \tn 
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% Row 4
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\mymulticolumn{1}{x{5.377cm}}{- {\bf{Backward elimination}} starts with all predictors and removes the least significant variable for each step.} \tn 
% Row Count 11 (+ 3)
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Regularized Linear Models (Shrinkage)}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Regularize linear model through constraining the weights} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Regularized term added to cost function. Learning algorithm not only fits data but keeps model weights as small as possible.} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Ridge}} (L2) | {\bf{Lasso}} (L1) | {\bf{ElasticNet}} (L1 \& L2)} \tn 
% Row Count 7 (+ 2)
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Ridge Regression}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{L1: adds penalty equivalent to {\bf{squ. of the magnitude}} of coefficients} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Minimization = LS Obj + α * (sum of squ of coefficients)} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{It shrinks the value of coefficients but doesn't reaches zero} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Lasso Regression}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{L1: adds penalty equivalent to {\bf{abs. value of the magnitude}} of coefficients} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Minimization = LS Obj + α * (sum of abs value of coefficients)} \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{LS Obj - Least Squares objective}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{ElasticNet Regression}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Ridge and Lasso: 'r' controls de mix ratio.} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{r*λ*sum(β\textasciicircum{}2\textasciicircum{}) +(1-r/2)* λ*sum(abs(β))} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Regression Types}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/isantabarbara_1518535493_Regression_Type[1].png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}Techniques are mostly driven by three metrics}  \tn 
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\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Linear Regression (Y=a+b*X + e)}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Straight line (regression line)} \tn 
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% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Least Square Method to best fit line} \tn 
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\mymulticolumn{1}{x{5.377cm}}{Linear relationship between predictors and target} \tn 
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\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}CONS} \tn 
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\mymulticolumn{1}{x{5.377cm}}{Multicollinearity, autocorrelation, heteroskedasticity} \tn 
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% Row 5
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\mymulticolumn{1}{x{5.377cm}}{Very sensitive to Outliers} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Logistic Regression}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Target binary (0/ 1): binomial distribution} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Logit function} \tn 
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\mymulticolumn{1}{x{5.377cm}}{widely used for classification problems} \tn 
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\mymulticolumn{1}{x{5.377cm}}{can handle various types of relationships because it applies a non-linear log transformation to the predicted odds ratio} \tn 
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% Row 4
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\mymulticolumn{1}{x{5.377cm}}{maximum likelihood estimates} \tn 
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\mymulticolumn{1}{x{5.377cm}}{Requires large sample sizes} \tn 
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% Row 6
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\mymulticolumn{1}{x{5.377cm}}{Ordinal Target -\textgreater{} Ordinal logistic regression} \tn 
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% Row 7
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\mymulticolumn{1}{x{5.377cm}}{Multiclass Target -\textgreater{} Multinomial Logistic regression.} \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Logistic Regression}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/isantabarbara_1518610460_Logistic_Regression[1].png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Logistic Regression}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{odds= p/ (1-p) \#event prob / not event prob \newline ln(odds) = ln(p/(1-p)) \newline logit(p) = ln(p/(1-p))  = \seqsplit{b0+b1X1+b2X2+b3X3....+bkXk}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{p is the probability of presence of the characteristic of interest.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}