negative correlation - how? - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

negative correlation - how?

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kunalkulkarni: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Mon May 07, 2012 10:59 am; Thanked: 2 times

by kunalkulkarni » 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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Source: Beat The GMAT — Data Insights | Sat Feb 09, 2013 5:23 pm

hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » 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.

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

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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kunalkulkarni: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Mon May 07, 2012 10:59 am; Thanked: 2 times

by kunalkulkarni » 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

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hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » 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.

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

by Tommy Wallach » 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.

Tommy Wallach, Company Expert
ManhattanGMAT

If you found this posting mega-helpful, feel free to thank and/or follow me!

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kunalkulkarni: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Mon May 07, 2012 10:59 am; Thanked: 2 times

by kunalkulkarni » Sun Feb 10, 2013 11:38 pm

Thank you Hemant and Tommy. Appreciate your help.

Cheers,
Kunal

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mkdureja: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Fri Jan 04, 2013 12:55 am; Thanked: 11 times

by mkdureja » 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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Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

by Tommy Wallach » 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

Tommy Wallach, Company Expert
ManhattanGMAT

If you found this posting mega-helpful, feel free to thank and/or follow me!

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tabsang: Senior | Next Rank: 100 Posts; Posts: 64; Joined: Mon Jun 13, 2011 5:27 am; Thanked: 5 times

by tabsang » Tue Sep 17, 2013 9:14 pm

Hey Kunal,

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

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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