In: Statistics and Probability
The following bivariate data set contains an outlier.
x | y |
---|---|
44.3 | 187 |
58.2 | 239.6 |
42 | 341.2 |
42.4 | -358.8 |
47.9 | -347.1 |
47.8 | 103 |
55 | 95.5 |
47.4 | -146.3 |
31.9 | 698.6 |
68.2 | -477.3 |
52.6 | -363.4 |
63.1 | 569.2 |
56 | -203.7 |
74.8 | 545.3 |
203.5 | 4226.3 |
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?
what are the steps on how to do it on a TI 84 calculator ?
Solution:
What is the correlation coefficient with the
outlier?
rw = 0.905989
(by using excel or Ti-84)
What is the correlation coefficient without the
outlier?
rwo = -0.03936
(by using excel or Ti-84 )
[Note, for the given data, the outlier observation is given as (203.5, 4226.3). Calculate correlation coefficient by deleting this observation.]
Would inclusion of the outlier change the evidence for or against a significant linear correlation?
(because as we see, when there is no outlier, there is a very low negative relationship exists; but when outlier exists, then it shows high positive linear relationship. )
Ti-84 steps for finding correlation are given as below:
Press 2nd and then 0, you will enter your calculators catalog.
Scroll down to diagnosticOn.
Press Enter. You will get screen message ‘Done’.
Then Enter data into calculator by pressing STAT and then selecting 1:Edit.
ENTER X data in L1
ENTER Y data in L2
Then, go to STAT, then press CALC
Select 4: LinReg
Press ENTER
You will get the value for correlation coefficient.