Question

In: Statistics and Probability

The following bivariate data set contains an outlier. x y 44.3 187 58.2 239.6 42 341.2...

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?

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


what are the steps on how to do it on a TI 84 calculator ?

Solutions

Expert Solution

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?

  • Yes. Including the outlier changes the evidence regarding a 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.


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