The following bivariate data set contains an outlier. What is the correlation co

Question

The following bivariate data set contains an outlier.

What is the correlation coefficient with the outlier?
rw =

What is the correlation coefficient without the outlier?
rwo =

Would inclusion of the outlier change the evidence for or against a significant linear correlation?

Yes. Including the outlier changes the evidence regarding a linear correlation.

No. Including the outlier does not change the evidence regarding a linear correlation.

Question for thought: Would you always draw the same conclusion with the addition of an outlier?

x y 41.1 -295.9 26.5 504.6 25.3 299.1 42.9 206 40.1 -94.9 34.3 -177.3 43 197.1 38.6 -149.2 42.6 400.9 28 531.4 30 -1044.4 24.3 -102.3 45 487.7 49.6 322.4 125.5 85

Explanation / Answer

The R code to remove outliers and to find the correlation with and without out liers.......

#define a function to remove the outliers from a vector

rm_outlr<- function(z, na.rm = TRUE, ...) {
qrtl <- quantile(x, probs=c(.25, .75), na.rm = na.rm, ...)
e <- 1.5 * IQR(z, na.rm = na.rm)
z1 <- z
z1[z < (qrtl[1] - e)] <- NA
z1[z > (qrtl[2] + e)] <- NA
z1
}
#given data

x<-c(41.1,26.5,25.3,42.9,40.1,34.3,43,38.6,42.6,28,30,24.3,45,49.6,125.5)
y<-c(-295.9,504.6,299.1,206,-94.9,-177.3,197.1,-149.2,400.9,531.4,-1044.4,-102.3,487.7,322.4,85)
x1<- rm_outlr(x) #data of x without outliers
y1<- rm_outlr(y) #data of y without outliers
x1 <- x1[!is.na(x1)] #remove NA values
y1 <- y1[!is.na(y1)] #remove NA values
cor(x,y)
cor(x1,y1)

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Answers..

> cor(x,y)
[1] 0.05350603
> cor(x1,y1)
[1] -0.3614671

here we can see that with outliers in the data , it seems there is almost zero correlation between x and y ,which is rw= 0.05350603. But without outliers we can see that there is a negative correlation between X and Y ,i.e rwo=-0.3614671 .So we can see that if we add the qutliers it has an impact on the data.and we can say that including the outlier, changes the evidence regarding a linear correlation.

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