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% Document Info
\author{kayheartsuu (kayheartsuu)}
\pdfinfo{
  /Title (ap-statistics-unit-2.pdf)
  /Creator (Cheatography)
  /Author (kayheartsuu (kayheartsuu))
  /Subject (AP Statistics Unit 2 Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    {\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{AP Statistics Unit 2 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{kayheartsuu (kayheartsuu)} via \textcolor{DarkBackground}{\uline{cheatography.com/162660/cs/34375/}}}
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\noindent
\begin{multicols}{3}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}kayheartsuu (kayheartsuu) \\
  \uline{cheatography.com/kayheartsuu} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 28th February, 2024.\\
   Updated 3rd November, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{3.68 cm} x{4.32 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Terms to Know}}  \tn
% Row 0
\SetRowColor{LightBackground}
scatterplot & display the relationship between two numerical variables \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
correlation coefficient "r" & the strength, direction, and linear relationship between the x-variable and y-variable \tn 
% Row Count 8 (+ 5)
% Row 2
\SetRowColor{LightBackground}
least square regression line & line of best fit for the scatterplot; minimizes the sum of the square of the deviations from a line \tn 
% Row Count 13 (+ 5)
% Row 3
\SetRowColor{white}
explanatory variable & explains the other variable; causes the response variable to change \tn 
% Row Count 17 (+ 4)
% Row 4
\SetRowColor{LightBackground}
response variable & response to the other variable; dependant \tn 
% Row Count 19 (+ 2)
% Row 5
\SetRowColor{white}
extrapolation & not right; using LSRL to predict values outside of the range of the original data set \tn 
% Row Count 24 (+ 5)
% Row 6
\SetRowColor{LightBackground}
outliers & points that are far away from the LSRL relative to other points \tn 
% Row Count 27 (+ 3)
% Row 7
\SetRowColor{white}
influential points & points that significantly impacts the slope of the LSRL \tn 
% Row Count 30 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.68 cm} x{4.32 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Terms to Know (cont)}}  \tn
% Row 8
\SetRowColor{LightBackground}
lurking variable & different outside variables that causes both x and y to change \tn 
% Row Count 3 (+ 3)
% Row 9
\SetRowColor{white}
residual & y - ŷ \tn 
% Row Count 4 (+ 1)
% Row 10
\SetRowColor{LightBackground}
coefficient of determination "r\textasciicircum{}2" & r\textasciicircum{}2\% of the variation in y-variable can be explained by the approximate linear relationship between x-variable and y-variable \tn 
% Row Count 10 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.2 cm} x{4.8 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Strength of "r" (Correlation Coefficient)}}  \tn
% Row 0
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legitimate values & {[}-1,1{]} \tn 
% Row Count 2 (+ 2)
% Row 1
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none & 0 \tn 
% Row Count 3 (+ 1)
% Row 2
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weak & (-0.5,0) U (0, 0.5) \tn 
% Row Count 4 (+ 1)
% Row 3
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moderate & (-0.8, -0.5) U (0.5, 0.8) \tn 
% Row Count 6 (+ 2)
% Row 4
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strong & {[}-1, -0.8) U 90.8, 1{]} \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{LSRL Example}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/kayheartsuu_1664337338_regression lsrl chart.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 202020 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship. \newline  \newline This is computer output from a least-squares regression analysis on the data.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{LSRL Example Interpretations}}  \tn
% Row 0
\SetRowColor{LightBackground}
find the LSRL & ŷ = 2.544 + 0.164x \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
identify the variables & x = amount of caffeine intake (mg); y = number hours spent studying \tn 
% Row Count 5 (+ 4)
% Row 2
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interpret the slope & when the amount of caffeine intake increases by one, the number of hours spent studying increase by 0.164 \tn 
% Row Count 11 (+ 6)
% Row 3
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identify the coefficient of determination & r\textasciicircum{}2 = 60.032 \tn 
% Row Count 14 (+ 3)
% Row 4
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interpret the coefficient of determination & 60.032\% of the variation in the amount of hours spent studying can be explained by the approximate linear relationship with caffeine intake \tn 
% Row Count 21 (+ 7)
% Row 5
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find the correlation coefficient & r = 0.7748 \tn 
% Row Count 23 (+ 2)
% Row 6
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interpret the correlation coefficient & there is a moderately strong, positive, linear relationship between the intake of caffeine and the amount of time spent studying \tn 
% Row Count 30 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.28 cm} x{4.72 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Interpretations}}  \tn
% Row 0
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slope of LSRL & for each increase in the "x-variable" of one "x-unit", there is a predicted "increase/decrease" in the "y-variable" of "b constant" "y-units" \tn 
% Row Count 7 (+ 7)
% Row 1
\SetRowColor{white}
correlation coefficient & there is a "strength", "direction", linear relationship between "x-variable" and "y-variable" \tn 
% Row Count 12 (+ 5)
% Row 2
\SetRowColor{LightBackground}
correlation of determination & "r\textasciicircum{}2"\% of the variation in the "y-variable" can be explained by the approximate linear relationship between "x-variable" and "y-variable" \tn 
% Row Count 18 (+ 6)
% Row 3
\SetRowColor{white}
residual & the actual "y-variable" is "residual" "y-unit" "above/below" the predicted "y-variable" \tn 
% Row Count 22 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Residuals and Residual Plots}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{the sum of the residual is always zero} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{error = observed - predicted} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{residual plots show if the model is appropriate or not between two variables} \tn 
% Row Count 4 (+ 2)
% Row 3
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\mymulticolumn{1}{x{8.4cm}}{if there is no pattern between the points on the residual plot, the model is appropriate} \tn 
% Row Count 6 (+ 2)
% Row 4
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\mymulticolumn{1}{x{8.4cm}}{if there is a pattern between the points on the residual plot, the model is not appropriate} \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{when the residual plot is not appropriate, you can transform the data points until the plot turns random} \tn 
% Row Count 11 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Residual Plot Examples}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/kayheartsuu_1664337135_residual plot.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{the top residual plot is appropriate because the points are random while the bottom residual plot is not appropriate because there is a pattern between the points}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Non-Linear Transform Data}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{x \& log y} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{log x \& log y} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{x \& sqrt y} \tn 
% Row Count 3 (+ 1)
% Row 3
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\mymulticolumn{1}{x{8.4cm}}{x \& 1/y} \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Correlation Doesn't Imply Causation}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/kayheartsuu_1664338573_correlation doesnt imply causation.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{If we collect data for the total number of Master's degrees issued by universities each year and the total box office revenue generated by year, we would find that the two variables are highly correlated.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Correlation Doesn't Imply Causation Explanation}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Does this mean that issuing more Master's degrees is causing the box office revenue to increase each year?  Not quite. The more likely explanation is that the global population has been increasing each year, which means more Master's degrees are issued each year and the sheer number of people attending movies each year are both increasing in roughly equal amounts.   Although these two variables are correlated, one does not cause the other.} \tn 
% Row Count 9 (+ 9)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}