Coefficient with and without the outlier

Question

The following bivariate data set contains an outlier.

xy
81.6	-289.2
73.5	-662.8
81.6	2509.5
65.8	-975
75.8	768.7
72.9	1757.9
93.6	146.2
83.8	-2578.9
111.2	81.7
82.6	-277.5
90.5	3624
91.2	-321.9
76.5	1131.8
78.5	-3051.2
247.4	451.1

What is the correlation coefficient with the outlier? 

r_w = 

What is the correlation coefficient without the outlier? 

r_wo = 

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

1. No. Including the outlier does not change the evidence regarding a linear correlation.
2. Yes. Including the outlier changes the evidence regarding a linear correlation.

Answer 1

If you create a scatterplot of the data, you'll quickly see that the point (247.4, 451.1) is significantly set off from the rest of the points and is likely the outlier.

The best way to calculate correlation is to use technology. I'd recommend typing the data into Excel and then using the function CORREL to find the correlation of the data with the outlier (approximately 0.07) and without the outlier (approximately 0.11).

Generally, you need a correlation that is close to +1 or -1 to indicate any strong evidence of a linear correlation, and any correlation between -0.3 and +0.3 is likely uncorrelated. The correlation without the outlier isn't any stronger then the one with.