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10012012, 10:52 AM  #1 (permalink) 
Bruins World Order  Math Question (Summation of 2 sets of data)
Alright, debating with someone and I need a math person: Given 2 sets of data (10 values each) so X and Y, how would you solve for the following: (Summation Sign)XY It's the sum of X times Y right? So how would you solve for it? 
10012012, 12:55 PM  #2 (permalink) 
What should I put here? Join Date: Dec 2008 
The way you have that equation written out, I would read it as SUM(X*Y). So you would multiply all the X's times their corresponding Y's, and add up all the products. Or, for the visually inclined: X1Y1 + X2Y2 + X3Y3 + X4Y4 + X5Y5 + X6Y6 + X7Y7 + X8Y8 + X9Y9+ X10Y10 Of course, I say that under the assumption that the scores are somehow corresponding to one another, such as in a correlation. The original post wasn't 100% clear on that point (or perhaps I'm just not reading it properly).
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10012012, 01:00 PM  #3 (permalink) 
Bruins World Order 
AHA! I KNEW IT! So my TA is indeed a dingbat and I'm not silly. This is great news. The scenario is: The X set is the values of cigarettes smoked by 10 Americans daily, Y is the values of cigarettes smoked by 10 Europeans daily. The questions were sumXY (Sum of X times Y) sumXsumY (Sum of X times Sum of Y) sumXY  sumXsumY/N over N1 (I hate math)
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10012012, 02:16 PM  #4 (permalink)  
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Another statistic is the covariance sigmaxy defined by: sigmaxy = [(x1  mux)(y1  muy) + ... + (xn  mux)(yn  muy)]/n = (x1y1 + ... + xnyn)/n  muxmuy. This is a measure of how much changes in x are associated with changes in y. If sigmaxy > 0 then x and y tend to increase or decrease together. If sigmaxy < 0, then y tends to decrease as x increases, and vice versa. If sigmaxy = 0, or is very small, then x and y tend to be independent of each other. What class is this for? been awhile since I had to do any of this. Might want to watch this How To Calculate Covariance (Math) I made a quick example in excel looking for the 3 explanations. I think this is accurate. X Y XY 1 2 2 2 2 4 3 2 6 4 2 8 5 2 10 6 2 12 7 2 14 8 2 16 9 2 18 sumx 45 sumy 18 sumXY 90 sumXY/n 10 sumXY/n/n1 1.25 Last edited by Harbinger[TG]; 10012012 at 02:25 PM.  
10012012, 02:30 PM  #5 (permalink) 
BEES BEES BEES  Linear Regression  Math@TutorVista.com Question: 10 observations on price X and supply "Y" the following data was obtained [sum] X = 130, [sum] Y = 220, [sum] X2 = 2288, [sum] 2 = 5506, [sum] XY = 3467 Find the line of regression of Y on X. Solution: The line of regression of Y on X Y = a + bX The norm equations are [sum] Y = a + b [sum] X [sum] XY =a [sum] X + b [sum] X2 10a + 130b = 220 ...........(i) 130a + 2288b = 3467 ..................(ii) Solving the equations (i) and (ii), we get a = 8.8 and b =1.01 => Y = 8.8 + (1.01)X 
10012012, 02:32 PM  #6 (permalink)  
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10012012, 03:29 PM  #7 (permalink) 
MCB Member Join Date: Jan 2010 Location: San Fran now 
it is unclear since the index is not labeled I would argue that the two sets Of data use separate indices, eventhough they are the same size. Therefore it would be the product of the sums of the sets of data separately(ie sumx times sumy) But it should have two sigmas with different index labels to be clear.
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10012012, 05:03 PM  #8 (permalink) 
Bruins World Order 
Thanks for the explanation guys. The math was done just for the sake of doing it, as the question was on an evaluation. The TA docked me 7/8 marks for not following the proper format but I knew I was right. It's for a 2nd year Social Sciences Statistics class. 
10012012, 05:51 PM  #10 (permalink)  
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