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  /Title (r-t2-3-analisis-de-la-correlacion.pdf)
  /Creator (Cheatography)
  /Author (julenx)
  /Subject (R T2.3 Análisis de la correlación Cheat Sheet)
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{R T2.3 Análisis de la correlación Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{julenx} via \textcolor{DarkBackground}{\uline{cheatography.com/168626/cs/35688/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}julenx \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 29th November, 2022.\\
   Updated 25th November, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Coeficiente de correlación de Pearson}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Debe satisfacer las siguientes condiciones} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}La relación que se quiere estudiar entre ambas variables es lineal \{\{nl\}\} Las dos variables deben de ser cuantitativas \{\{nl\}\}  Normalidad: ambas variables se tienen que distribuir de forma normal (test K-S) \{\{nl\}\} Homocedasticidad: La varianza de 𝑌 debe ser constante a lo largo de la variable 𝑋 (test de Bartlett)} \tn 
% Row Count 8 (+ 8)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Características} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Toma valores entre {[}-1, +1{]}, siendo +1 una correlación lineal positiva perfecta y -1 una correlación lineal negativa perfecta. Si es 0 significa que NO existe relación lineal entre las variables consideradas. \{\{nl\}\}  No varía si se aplican transformaciones a las variables \{\{nl\}\} no equivale a la pendiente de la recta de regresión \{\{nl\}\} es necesario calcular su significatividad (p-valor)  si no es significativo, se ha de interpretar que la correlación de ambas variables es 0} \tn 
% Row Count 20 (+ 12)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{1.1. Evidencias gráficas: Scatterplot}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}library(ggplot2) \{\{nl\}\} ggplot(data = Cars93, \{\{nl\}\} ~ aes(x = Weight, y = Horsepower)) +  \{\{nl\}\} ~ geom\_point(colour = "red4") +  \{\{nl\}\} ~ ggtitle("Diagrama de dispersión") +  \{\{nl\}\} ~ theme\_bw() +  \{\{nl\}\} ~ theme(plot.title = element\_text(hjust = 0.5))} \tn 
% Row Count 27 (+ 7)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{1.2. Evidencias gráficas: Análisis de normalidad}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}par(mfrow = c(1, 2)) \{\{nl\}\} hist(Cars93\$Weight, breaks = 10, main = "", \{\{nl\}\} ~ xlab = "Weight", border = "darkred") \{\{nl\}\} hist(Cars93\$Horsepower, breaks = 10, main = "", \{\{nl\}\} ~ xlab = "Horsepower", border = "blue") \{\{nl\}\} par(mfrow = c(1, 1))} \tn 
% Row Count 35 (+ 8)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Coeficiente de correlación de Pearson (cont)}}  \tn
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{1.3. Evidencias gráficas: gráfico quantil-quantil (Q-Q plot)}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}qqnorm(Cars93\$Weight, main = "Weight", \{\{nl\}\} ~ col = "darkred") \{\{nl\}\} qqline(Cars93\$Weight) \{\{nl\}\} \seqsplit{qqnorm(Cars93\$Horsepower}, main = "Horsepower", \{\{nl\}\} ~ col = "blue")  \{\{nl\}\} \seqsplit{qqline(Cars93\$Horsepower)}} \tn 
% Row Count 7 (+ 7)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}par(mfrow = c(1, 2)) \{\{nl\}\} qqnorm(Cars93\$Weight, main = "Weight", \{\{nl\}\} ~ col = "darkred")  \{\{nl\}\} qqline(Cars93\$Weight) \{\{nl\}\} \seqsplit{qqnorm(Cars93\$Horsepower}, main = "Horsepower", \{\{nl\}\}  ~  col = "blue")  \{\{nl\}\} \seqsplit{qqline(Cars93\$Horsepower)} \{\{nl\}\} par(mfrow = c(1, 1))} \tn 
% Row Count 13 (+ 6)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{2.1 Evid. contr.: test K-S-L}} (H0= dist. normal)} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}require(nortest) \{\{nl\}\} \seqsplit{lillie.test(Cars93\$Weight)} \{\{nl\}\} \seqsplit{lillie.test(Cars93\$Horsepower)}} \tn 
% Row Count 17 (+ 4)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{2.2 Si no es dist. normal: tipificación}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}a cada observación se resta la media y se divide por la desviación típica. \{\{nl\}\} xt = scale(x)} \tn 
% Row Count 21 (+ 4)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{2.3 Si no es dist. normal: transformación no lineal}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Asimetría negativa: 𝑥2 \{\{nl\}\} Asimetría positiva: √𝑥 (poco) 𝑙𝑛(𝑥) (medio) 1/𝑥 (alto) \{\{nl\}\} Ahora se repiten todos los pasos a partir de evidencias gráficas: normalidad} \tn 
% Row Count 28 (+ 7)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{3.1. Análisis de la homocedasticidad: Gráficas}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}ggplot(data = Cars93, aes(x = Weight, \{\{nl\}\} ~ y = Horsepower)) +  geom\_point(colour = "red4") + \{\{nl\}\} ~ geom\_segment(aes(x = 1690, y = 70, xend = 3100, \{\{nl\}\} ~ yend = 300), linetype = "dashed") + \{\{nl\}\} ~ geom\_segment(aes(x = 1690, y = 45, xend = 4100, \{\{nl\}\} ~ yend = 100),linetype = "dashed") + \{\{nl\}\} ~ ggtitle("Diagrama de dispersión") + theme\_bw() + \{\{nl\}\} ~ theme(plot.title = element\_text(hjust = 0.5))} \tn 
% Row Count 40 (+ 12)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Coeficiente de correlación de Pearson (cont)}}  \tn
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{3.2. Análisis de la homocedasticidad: ev. cont. test de Bartlett}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}El p-valor menor que  5\%  permite rechazar la hipótesis nula  𝐻0 \{\{nl\}\}bartlett.test(list(Cars93\$Weight,Cars93\$Horsepower)) \{\{nl\}\} Test de Bartlett en las variables transformadas \{\{nl\}\} \seqsplit{bartlett.test(list(log(Cars93\$Weight)},log(Cars93\$Horsepower)))} \tn 
% Row Count 8 (+ 8)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{4.1. Coeficiente de Pearson (ev. num. solo)}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}cor(x = Cars93\$Weight, y = log(Cars93\$Horsepower), method = "pearson")} \tn 
% Row Count 11 (+ 3)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{4.2. Coeficiente de Pearson (ev. contrastada)}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Comrpobamos que p-valor sea menor que o igual que 0,05 \{\{nl\}\} cor.test(x = Cars93\$Weight, y = log(Cars93\$Horsepower),alternative = "two.sided",conf.level = 0.95, method = "pearson")} \tn 
% Row Count 16 (+ 5)
% Row 13
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{5. Coeficiente de determinación  𝑅2}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}cantidad de varianza de la variable 𝑌 explicada por 𝑋 y que se obtiene elevando al cuadrado el coeficiente de correlación  𝑟  \{\{nl\}\} El  𝑅2  presenta valores entre 0 y 1. Lo más próximo a 1 significará que con nuestra variable X seremos capaces de explicar en gran medida el comportamiento de nuestra variable Y. En cambio, si se aproxima a 0 querrá decir que si nuestro objetivo es explicar la variable Y en función de X, tendremos que cambiar de variable explicativa (X) ya que prácticamente no nos aporta información sobre la variable Y.} \tn 
% Row Count 29 (+ 13)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Si no se cumplen condiciones del coef. Pearson}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Coeficiente Rho de Spearman}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Cuando estamos ante variables categóricas (no numéricas) (género y educación) \{\{nl\}\} Cuando los valores no pertenecen a una distribución normal} \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{require(MASS)} \tn 
% Row Count 6 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{cor.test(birthwt\$bwt, birthwt\$lwt, alternative="two.sided", method="spearman")} \tn 
% Row Count 8 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cor.test(birthwt\$bwt, birthwt\$lwt, alternative="less", method="spearman")} \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{cor.test(birthwt\$bwt, birthwt\$lwt, alternative="greater", method="spearman")} \tn 
% Row Count 12 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Coeficiente Tau de Kendall}}} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Cuando estamos ante variables categóricas (no numéricas) (género y educación) \{\{nl\}\} Cuando los valores no pertenecen a una distribución normal} \tn 
% Row Count 17 (+ 5)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{require(MASS)} \tn 
% Row Count 18 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cor.test(birthwt\$bwt, birthwt\$lwt, alternative="two.sided", method="kendall")} \tn 
% Row Count 20 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{etc} \tn 
% Row Count 21 (+ 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}{La matriz de correlaciones}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{cor(x = datos, method = "pearson")} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{pairs(x = datos, lower.panel = NULL)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{require(corrplot)} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{corrplot(corr = cor(x = datos, method = "pearson"), method = "number")} \tn 
% Row Count 5 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{require(psych)} \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{pairs.panels(x = datos, ellipses = FALSE, lm = TRUE, method = "pearson")} \tn 
% Row Count 8 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{El coeficiente de correlación parcial}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Se quiere estudiar la relación entre las variables precio y peso de los automóviles. Se sospecha que esta relación podría estar influenciada por la variable potencia del motor, ya que a mayor peso del vehículo se requiere mayor potencia y, a su vez, motores más potentes son más caros.} \tn 
% Row Count 6 (+ 6)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{ggplot(data = Cars93, aes(x = Weight, y = log(Price))) + \{\{nl\}\} geom\_point(colour = "red4") + \{\{nl\}\} ggtitle("Diagrama de dispersión") + theme\_bw() + \{\{nl\}\}  theme(plot.title = element\_text(hjust = 0.5))} \tn 
% Row Count 11 (+ 5)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{cor.test(x = Cars93\$Weight, y = log(Cars93\$Price), method = "pearson")} \tn 
% Row Count 13 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{require(ppcor) \{\{nl\}\} pcor.test(x = Cars93\$Weight, y = log(Cars93\$Price), \{\{nl\}\} ~ z = Cars93\$Horsepower, method = "pearson")} \tn 
% Row Count 16 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{La correlación entre el peso y el logaritmo del precio es alta (r=0.764) y significativa (p-value \textless{} 2.2e-16). Sin embargo, cuando se estudia su relación bloqueando la variable potencia de motor, a pesar de que la relación sigue siendo significativa (p-value = 6.288649e-05) pasa a ser baja (r=0.4047). \{\{nl\}\} Luego, podemos concluir que la relación lineal existente entre el peso y el logaritmo del precio está influenciada por el efecto de la variable potencia de motor. Si se controla el efecto de la potencia, la relación lineal existente es baja (r=0.4047).} \tn 
% Row Count 28 (+ 12)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}