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negative correlation - how?

This topic has 2 expert replies and 6 member replies
kunalkulkarni Senior | Next Rank: 100 Posts Default Avatar
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negative correlation - how?

Post Sat Feb 09, 2013 5:23 pm
there are 2 sets of data:
X = {0,0,0,4,4,4,6,6,8}
Y = {50,38,56,34,32,42,28,34,29}
There is a negative correlation between X and Y.

Can anyone please explain me. how is the above statement true?
My understanding is as follows:
positive correlation - directly proportional
negative correlation - inversely proportional

Please help me with above question.
Thanks in advance,
Kunal

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hemant_rajput Master | Next Rank: 500 Posts
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Post Sun Feb 10, 2013 5:56 am
kunalkulkarni wrote:
there are 2 sets of data:
X = {0,0,0,4,4,4,6,6,8}
Y = {50,38,56,34,32,42,28,34,29}
There is a negative correlation between X and Y.

Can anyone please explain me. how is the above statement true?
My understanding is as follows:
positive correlation - directly proportional
negative correlation - inversely proportional

Please help me with above question.
Thanks in advance,
Kunal
Hi kunal,

Your understanding of negative correlation is perfect. Here, we have two sets, X and Y. These two sets are in negative correlation because, with every increase in the value of element in X, value of element in Y is decreasing.


0 - 50************************
***********0 - 38 ************
************************0 - 56
4 - 34************************
***********4 - 32*************
************************4 - 42
6 - 28************************
***********6 - 34*************
************************8 - 29


I hope this pictorial representation will make it easy for you to comprehend.

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Last edited by hemant_rajput on Sun Feb 10, 2013 8:33 pm; edited 1 time in total

kunalkulkarni Senior | Next Rank: 100 Posts Default Avatar
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Post Sun Feb 10, 2013 12:15 pm
Hey Hemant,
Thank you for the reply.
So the main catch is to find the transitioning numbers as X changes from 0 to 6. Just to ensure I understood it correctly, if below was the series for X and Y
0 - 50
0 - 38

4 - 42
4 - 36

6 - 32
6 - 40

then it would be impossible to find negative or positive correlation. right?

Thanks,
Kunal

hemant_rajput Master | Next Rank: 500 Posts
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Post Sun Feb 10, 2013 8:34 pm
Hi Kunal,

I did some modification in pictorial representation in my previous post. I guess BTG post skips white space in forum. Hope this make it clear.

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Tommy Wallach GMAT Instructor
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Post Sun Feb 10, 2013 10:45 pm
Hey Kunal,

You are correct. In that set, there wouldn't be a correlation you could call either positive or negative.

-t

P.S. Indeed, BtG does not like white spaces in posts. It's a bit like trying to leave silence on your iPhone voice mail. Ever tried it? No dice.

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kunalkulkarni Senior | Next Rank: 100 Posts Default Avatar
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Post Sun Feb 10, 2013 11:38 pm
Thank you Hemant and Tommy. Appreciate your help.

Cheers,
Kunal

mkdureja Senior | Next Rank: 100 Posts Default Avatar
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Post Thu Feb 14, 2013 12:55 am
As per my understanding, correlation is a statistical term with a proper formula. Its value varies from -1 to +1 for any set of data, with value of +1 representing perfect linear positive correlation (data set will draw a straight line in cartesian plane), similarly -1 represents a straight line with negative slope.
Basically, for any given set of data, even random, correlation will be either positive or negative, close to zero for highly uncorrelated/random data.
In the above question, it is clear that when X increases, Y decreases, other than for some exceptions, which can be ignored.

This is my understanding, open for other explanations.

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Post Thu Feb 14, 2013 9:31 am
Hey Mk,

While all that you said may be true, advanced statistics aren't really tested on the GMAT. So you don't need to know much other than a pure positive or a pure negative correlation (i.e. When X goes up, Y goes up; or when X goes down, Y goes up).

-t

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tabsang Senior | Next Rank: 100 Posts
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Post Tue Sep 17, 2013 9:14 pm
Hey Kunal,

Could you please elaborate on this.
I'm not quite sure that I got this Sad Sad

Cheers,
Taz

kunalkulkarni wrote:
Hey Hemant,
Thank you for the reply.
So the main catch is to find the transitioning numbers as X changes from 0 to 6. Just to ensure I understood it correctly, if below was the series for X and Y
0 - 50
0 - 38

4 - 42
4 - 36

6 - 32
6 - 40

then it would be impossible to find negative or positive correlation. right?

Thanks,
Kunal

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