Correlation... why between +/- 1
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hum... I been looking at how correlation is calculated for last few hours[^]... can't figure out why, mathematically, why correlation is bounded between [-1,+1]
dev
Haven't these mathematicians ever heard of variable naming conventions? Ya know, I've worked with calculation libraries written by math PhDs... It's all x, y, z, q, r, n, q1, n1, x1...
Proud to have finally moved to the A-Ark. Which one are you in?
Author of Guardians of Xen (Sci-Fi/Fantasy novel) -
yes... but look at the formula... I can't prove, mathematically, why -1< correlation <1
dev
Its like probability, when expressed between 0 and 1 (or -1 and 1) as opposed to percentages. 1 = 100% correlation 0 = 0 % correlation -1 = 100% inverse correlation. It wouldn't make sense to have a 200% correlation and keeping 100% correlation as 1 just makes it much easier.
Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
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Its like probability, when expressed between 0 and 1 (or -1 and 1) as opposed to percentages. 1 = 100% correlation 0 = 0 % correlation -1 = 100% inverse correlation. It wouldn't make sense to have a 200% correlation and keeping 100% correlation as 1 just makes it much easier.
Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
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Haven't these mathematicians ever heard of variable naming conventions? Ya know, I've worked with calculation libraries written by math PhDs... It's all x, y, z, q, r, n, q1, n1, x1...
Proud to have finally moved to the A-Ark. Which one are you in?
Author of Guardians of Xen (Sci-Fi/Fantasy novel) -
No, its defined that way (axiomatic), it follows the ternary logic of -1,0,1 and probabalistic systems of any number 0<= probaility <=1. The mathematicians could have chosed -100% -> + 100%, they would just have needed to multiply by 100, using 1 is the simplest form. Any proof you think you have is due to the fact the mathmaticians work in the range -1 <= correlation factor <=1.
Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
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hum... I been looking at how correlation is calculated for last few hours[^]... can't figure out why, mathematically, why correlation is bounded between [-1,+1]
dev
Yeah, it's not really that hard to figure out. If correlation equals = Pearson Correlation Picture[^] then, the values are bounded by 1 and -1. The numerator in the equation can be negative or positive depending on whether the numbers are less than or greater than the means. If it's a negative correlation, that means that the second set of numbers decreases while the first set increases. If it's positive, the second set increases as the first set increases. The equation y=25x-17 has a positive correlation, while the equation y=-25x-17 has a negative correlation. If you don't believe it, throw it into excel and run the numbers.
modified on Thursday, February 25, 2010 5:00 PM
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No, its defined that way (axiomatic), it follows the ternary logic of -1,0,1 and probabalistic systems of any number 0<= probaility <=1. The mathematicians could have chosed -100% -> + 100%, they would just have needed to multiply by 100, using 1 is the simplest form. Any proof you think you have is due to the fact the mathmaticians work in the range -1 <= correlation factor <=1.
Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
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Still, it should be provable that the formula given follows the axioms...
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Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
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No, its defined that way (axiomatic), it follows the ternary logic of -1,0,1 and probabalistic systems of any number 0<= probaility <=1. The mathematicians could have chosed -100% -> + 100%, they would just have needed to multiply by 100, using 1 is the simplest form. Any proof you think you have is due to the fact the mathmaticians work in the range -1 <= correlation factor <=1.
Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
comeon, doesn't take a mathematicians to prove it in range -1,+1. just look at the formula http://en.wikipedia.org/wiki/Correlation_and_dependence[^] and substitute the special case where X=Y (i.e. perfectly correlated) And, it's not probability - it's how two variables co-vary with each other.
dev
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Yeah, it's not really that hard to figure out. If correlation equals = Pearson Correlation Picture[^] then, the values are bounded by 1 and -1. The numerator in the equation can be negative or positive depending on whether the numbers are less than or greater than the means. If it's a negative correlation, that means that the second set of numbers decreases while the first set increases. If it's positive, the second set increases as the first set increases. The equation y=25x-17 has a positive correlation, while the equation y=-25x-17 has a negative correlation. If you don't believe it, throw it into excel and run the numbers.
modified on Thursday, February 25, 2010 5:00 PM
just look at the formula http://en.wikipedia.org/wiki/Correlation\_and\_dependence\[^\] and substitute the special case where X=Y (i.e. perfectly correlated), then do the math you'd get there.
dev
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comeon, doesn't take a mathematicians to prove it in range -1,+1. just look at the formula http://en.wikipedia.org/wiki/Correlation_and_dependence[^] and substitute the special case where X=Y (i.e. perfectly correlated) And, it's not probability - it's how two variables co-vary with each other.
dev
devvvy wrote:
comeon, doesn't take a mathematicians to prove it in range -1,+1.
:wtf: That is not a mathematical proof, which was my point here. What you describe is taking the formula derived by the mathematicians and working it back to their started from, i.e. that perfect correlation =1. If the mathematicians had used percentages instead, you'd work back and get 100%. You are right, it doesn't take a mathematician to work it back, but it does take a mathematician to understand what a mathematical proof is apparently.
devvvy wrote:
And, it's not probability - it's how two variables co-vary with each other.
Never said it was, I said it followed the same system , i.e. a pre-defined range where 1 forms the absolute upper bound. I used probability because the OP was like asking "Why is probability between 0 and 1?". The answer is really by convention, as we can also scale up to percentages, or by a factor of 42 or whatever you want, but 0-->1 remains the simplest form.
Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
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hum... I been looking at how correlation is calculated for last few hours[^]... can't figure out why, mathematically, why correlation is bounded between [-1,+1]
dev
You probably need to take the equation for standard deviation into account: http://en.wikipedia.org/wiki/Standard_deviation[^], and then toss the symbols about. Then I'm sure you can find a proof that the coefficient is bounded between -1 and 1 (with one or more constraints).
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