library(ggpubr)

ggscatter(mtcars, x = "mpg", y = "wt", 
          add = "reg.line", 
          conf.int = TRUE, 
          cor.coef = TRUE, 
          cor.method = "pearson",
          xlab = "Miles/(US) gallon", 
          ylab = "Weight (1000 lbs)")

#Shapiro-Wilk normality test for mpg and wt
shapiro.test(mtcars$mpg) 

shapiro.test(mtcars$wt) 

#Visual inspection of the data normality using Q-Q plots (quantile-quantile plots)
#Q-Q plot draws the correlation between a given sample and the normal distribution.
ggqqplot(mtcars$mpg, ylab = "MPG")

ggqqplot(mtcars$wt, ylab = "WT")

#Pearson correlation test
cor.test(mtcars$wt, mtcars$mpg, method = "pearson")

#Spearman rank correlation coefficient
cor.test(mtcars$wt, mtcars$mpg,  method = "spearman")

#Kendall rank correlation test
res <- cor.test(mtcars$wt, mtcars$mpg,  method="kendall")

#Extract the p.value and the correlation coefficient
res$p.value

res$estimate

#install.packages("corrplot")
library(corrplot)

#install.packages("Hmisc")
library(Hmisc)

#install.packages("ggcorrplot")
library(ggcorrplot)

corr <- round(cor(mtcars), 2) #Compute a correlation matrix
p.mat <- cor_pmat(mtcars) #Compute a matrix of correlation p-values

#corr <- rcorr(as.matrix(mtcars))
#head(round(corr$r, 2)) #Extract the correlation coefficients
#head(round(corr$P, 3)) #Extract p-values

### flattenCorrMatrix function
#cormat: matrix of the correlation coefficients
#pmat: matrix of the correlation p-values
flattenCorrMatrix <- function(cormat, pmat) {
  ut <- upper.tri(cormat)
  data.frame(
    row = rownames(cormat)[row(cormat)[ut]],
    column = rownames(cormat)[col(cormat)[ut]],
    cor  =(cormat)[ut],
    p = pmat[ut]
    )
}

#head(flattenCorrMatrix(corr$r, corr$P))

library(RColorBrewer)
col<- colorRampPalette(c("red", "white", "blue"))(20)

corrplot(corr, 
         method="circle", #visualization method
         type="upper", #types of layout
         order="hclust", #order: reorder the correlation matrix
         col=col, #col: Using different color spectrum
         #bg="lightblue", #bg: Change background color to lightblue
         #col=brewer.pal(n=8, name="RdBu") #use RcolorBrewer palette of colors
         #col=brewer.pal(n=8, name="RdYlBu") #use RcolorBrewer palette of colors
         #col=brewer.pal(n=8, name="PuOr") #use RcolorBrewer palette of colors
         tl.col="blue", #change text colors
         tl.srt=45, #change label rotations
         
         #Combine with significance
         p.mat = p.mat, #add the matrix of p-value
         sig.level = 0.01, ## Specialized the insignificant value according to the significant level
         insig = "blank", #Leave blank on no significant coefficient
         
         diag=FALSE #hide correlation coefficient on the principal diagonal
         )

#install.packages("PerformanceAnalytics")
library("PerformanceAnalytics")

my_data <- mtcars[, c(1,3,4,5,6,7)]
chart.Correlation(my_data, histogram=TRUE, pch=19)

#The distribution of each variable is shown on the diagonal.
#left bottom of the diagonal: the bivariate scatter plots with a fitted line are displayed
#right top of the diagonal: the value of the correlation plus the significance level as stars
#Each significance level is associated to a symbol: 
#p-values(0, 0.001, 0.01, 0.05, 0.1, 1) <=> symbols(***, **, *, ., ,"")

col <- colorRampPalette(c("blue", "white", "red"))(20)
heatmap(x = corr, col = col, symm = TRUE)

#x: the correlation matrix to be plotted
#col: color palettes
#symm: logical indicating if x should be treated symmetrically; can only be true when x is a square matrix.

ggcorrplot(corr, 
           method = "circle",  #"square" (default), "circle" 
           type = "lower", # "full" (default), "lower" or "upper" display.
           hc.order = TRUE, #logical value. If TRUE, correlation matrix will be hc.ordered using hclust function.
           outline.col = "white", #the outline color of square or circle. Default "gray"
           ggtheme = ggplot2::theme_classic, #Change theme
           colors = c("red", "white", "green"), #Change colors
           lab = TRUE, #Add correlation coefficients
           sig.level=0.05, #set significant level
           p.mat = p.mat, #Add correlation significance level
           insig = "blank" #Leave blank on no significant coefficient
           )

# install.packages("ppcor")
library(ppcor)

# calculate the correlations between each pair with all other variables are adjusted 
partial.corr <- pcor(x=mtcars, method="spearman")
#Results interpretation: ?pcor()

# calculate the correlations between each pair with specified variables are adjusted 
partial_correlation <- function(df) {
  n <- ncol(df)
  results <- list() # define an empty list
  results[["estimate"]] <- sapply(1:(n-3), function(x) {
    sapply(1:(n-3), function(y) {
      ifelse(x == y, 1, pcor.test(df[,x], df[,y], df[,c((n-2):n)], method="spearman")$estimate)
    })
  })
  results[["p.value"]] <- sapply(1:(n-3), function(x) {
    sapply(1:(n-3), function(y) {
      ifelse(x == y, 0, pcor.test(df[,x], df[,y], df[,c((n-2):n)], method="spearman")$p.value)
    })
  })
  colnames(results[["estimate"]]) <- rownames(results[["estimate"]]) <- colnames(df[, c(1:(n-3))])
  colnames(results[["p.value"]]) <- rownames(results[["p.value"]]) <- colnames(df[, c(1:(n-3))])
  return(results)
}

pcor <- partial_correlation(mtcars)

library(ggcorrplot)
ggcorrplot(pcor$estimate,
           method = "circle",  #"square" (default), "circle"
           type = "lower", # "full" (default), "lower" or "upper" display.
           hc.order = TRUE, #logical value. If TRUE, correlation matrix will be hc.ordered using hclust function.
           outline.col = "white", #the outline color of square or circle. Default "gray"
           ggtheme = ggplot2::theme_classic, #Change theme
           colors = c("red", "white", "green"), #Change colors
           lab = TRUE, #Add correlation coefficients
           sig.level=0.05, #set significant level
           p.mat = pcor$p.value, #Add correlation significance level
           insig = "blank", #Leave blank on no significant coefficient
           title = "Partial correlations for mtcars"
           )