6- Week 6 Lab Associations

1. Scatterplot and Loess smoother . Follow the attached template from the lecture notes and use Age on the x -axis and Weight on the y -axis. Include the linear relationship and the uncertainty associated with the loess smoother. Try to make this graph beautiful and include appropriate labels for the axes. Does this relationship appear linear, nonlinear, and/or monotonic? 2. Pearson, Spearman, and Distance Correlations. Compute these three correlations. How do these three estimates compare? Are they similar or different? Note that given the large sample size here (9922), the distance correlation function will be quite slow. Example Code for Figure and Analyses (on Canvas) #Creating a small example dataset to illustrate the code #for plots and obtaining correlation estimates. #Use your dataset instead of x and y below in this example. x <- rnorm( 200 ) y <- . 3 *x + rnorm( 200 ) example <- as.data.frame(cbind(x,y)) #Example of a loess plot with the uncertainty around the loess curve (se=TRUE) #This also adds the linear relationship (without the uncertainty, se=FALSE) library(ggplot2) ggplot(example, aes(x, y)) + geom_point( size = 0.70 ) + geom_smooth( method= "loess" , colour= "darkorchid4" , size= 1 , fill= "orchid4" , se= TRUE) + geom_smooth( method= "lm" , colour= "black" , size= . 75 , fill= "grey20" , se= FALSE) + labs( x= "This is the label for the x-axis" , y= "This is the label for the y-axis" ) + theme_classic() #Pearson and Spearman correlations cor(example$x, example$y, method= "pearson" ) cor(example$x, example$y, method= "spearman" ) #Distance correlation library(energy) dcorT.test(example$x, example$y) #Note that dcor.ttest() provides the squared correlation. #Take the square root to get the distance correlation sqrt(dcorT.test(example$x, example$y)$estimate) #Test where you estimate the p-value by simulating the #null hypothesis. R is the number of samples drawn under the null. #For very large sample sizes (N > 1000), start with smaller R values #to see how long it takes to run before increasing R. dcor.test(example$x, example$y, R= 1000 ) 2