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\author{Chrish0204}
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  /Title (logistic-regression-review.pdf)
  /Creator (Cheatography)
  /Author (Chrish0204)
  /Subject (Logistic Regression Review Cheat Sheet)
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Logistic Regression Review Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Chrish0204} via \textcolor{DarkBackground}{\uline{cheatography.com/21287/cs/4136/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Chrish0204 \\
  \uline{cheatography.com/chrish0204} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 10th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
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\begin{multicols*}{4}

\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Interpretation of Coefficients}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{{\bf{Beta-0}} \newline % Row Count 1 (+ 1)
- log(odds) when X1 = 0..., X-i = 0 \newline % Row Count 2 (+ 1)
- Often not intepretable (outside range of data) \newline % Row Count 3 (+ 1)
- Sometimes can be thought of as background odds \newline % Row Count 4 (+ 1)
{\bf{Beta-1}} \newline % Row Count 5 (+ 1)
- Difference in log(odds) for two groups differing in their level of X-1 by one unit, but otherwise similar for all other X-i (same as the log of the OR comparing these two groups) \newline % Row Count 9 (+ 4)
- Because of the properties of logoarthms, beta-1 is also the log of the odds ratio for two groups differing in their level of X-1 by one unit, but otherwise similar for all other X-i \newline % Row Count 13 (+ 4)
- (beta-1)(1) is the log odds ratio between two groups differing in X-1 by one unit, while (beta-1)(5) is the log odds ratio between two groups differing in X-1 by five units \newline % Row Count 17 (+ 4)
{\bf{e\textasciicircum{}beta-1}} \newline % Row Count 18 (+ 1)
- Odds ratio for two groups differing in their level of X-1 by one unit, but otherwise agreeing in their level of all other X-i \newline % Row Count 21 (+ 3)
- Similarly: (beta-1)(5) is the log(odds) between two groups different in their value of X-1 by 5, and e\textasciicircum{}(beta-1)(5) is the odds ratio between two such groups \newline % Row Count 25 (+ 4)
- (e\textasciicircum{}beta-1)(1) is OR comparing one unit apart, while (e\textasciicircum{}beta-1)*(5) is OR comparing five units apart% Row Count 28 (+ 3)
} \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Interaction Terms}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{- Relationship between X and Y is moderated through Z \newline % Row Count 2 (+ 2)
- This means the OR for Y between two groups that differ on X varies with Z \newline % Row Count 4 (+ 2)
log(odds(Y|X,Z)) = beta-0 + beta-X(X) + beta-Z(Z) + beta-XZ(X*Z) \newline % Row Count 6 (+ 2)
{\bf{Coefficient Interpretation}} \newline % Row Count 7 (+ 1)
- Beta-0 still log(odds) of Y, given all X-i are zero \newline % Row Count 9 (+ 2)
- Beta-X is difference in log(odds) of Y between two groups differing by one unit of X, when Z = 0 \newline % Row Count 11 (+ 2)
- Beta-Z is difference in log(odds) of Y between two groups differing by one unit of Z, when X = 0 \newline % Row Count 13 (+ 2)
- Possible that X and/or Z = 0 outside of range of data, but still need to include this \newline % Row Count 15 (+ 2)
{\bf{Interaction Term}} \newline % Row Count 16 (+ 1)
- BetaXZ is change in slope per 1 unit difference in X, comparing 1 unit differences in Z \newline % Row Count 18 (+ 2)
- e\textasciicircum{}beta(interaction) is ratio of the OR when interacting variable =1 compared to when interacting variable = 0 \newline % Row Count 21 (+ 3)
- "The interaction term is the difference in log(OR) comparing situations where the interacting variable differs by one unit." \newline % Row Count 24 (+ 3)
- Note that on the log scale, this is a difference, whereas on the OR scale, it is a ratio% Row Count 26 (+ 2)
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Model Fitting}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{- Model coefficients estimated by achieving "minimum deviance" \newline % Row Count 2 (+ 2)
- No general formula exists for this; software is needed to do this \newline % Row Count 4 (+ 2)
- The beta-hats identified through this process are called the maximum likelihood estimates (MLEs) of the true beta-0 and beta-1 \newline % Row Count 7 (+ 3)
{\bf{Likelihood Theory}} \newline % Row Count 8 (+ 1)
- Provides tools for converting modeling assumptions into SE estimates \newline % Row Count 10 (+ 2)
- Assumes that in population, Y and X really do have logistic relationship; however, can still get "best estimates" with minimum deviance (just no SEs/CIs) \newline % Row Count 14 (+ 4)
{\bf{Estimation Theory}} \newline % Row Count 15 (+ 1)
- Use robust estimates to obtain SEs/CIs of coefficients in the model, even when true population is not a logistic relationship \newline % Row Count 18 (+ 3)
- Point estimates will be same as model-based, but CIs are slightly different% Row Count 20 (+ 2)
} \tn 
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% That's all folks
\end{multicols*}

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