Correlation... why between +/- 1
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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...
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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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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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