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Old 10-01-2012, 10:52 AM   #1 (permalink)
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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?
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Old 10-01-2012, 12:55 PM   #2 (permalink)
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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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Old 10-01-2012, 01:00 PM   #3 (permalink)
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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 N-1 (I hate math)
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Last edited by StJimmy666; 10-01-2012 at 01:05 PM.
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Old 10-01-2012, 02:16 PM   #4 (permalink)
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Quote:
Originally Posted by StJimmy666 View Post
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?
If you are only referring to this "(Summation Sign)XY" then it should be the XY1+XY2+ etc etc. There is actually this What does Σxy mean (sigma xy)? - Yahoo! Answers


Quote:
Originally Posted by super_gman View Post
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).
I agree. I don't really see why one would be calculating this because the two data sets have nothing to do with another.

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Originally Posted by StJimmy666 View Post
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 N-1 (I hate math)
Yeah. i don't see how the two data sets are related and would require this. Unless it is just to do it for maths sake. Might want to also check this out Statistics

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/n-1 1.25
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Last edited by Harbinger[TG]; 10-01-2012 at 02:25 PM.
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Old 10-01-2012, 02:30 PM   #5 (permalink)
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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
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Old 10-01-2012, 02:32 PM   #6 (permalink)
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that is all...
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Old 10-01-2012, 03:29 PM   #7 (permalink)
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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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Old 10-01-2012, 05:03 PM   #8 (permalink)
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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.
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Seconded. Hence forth this is to be the official nomenclature of marker sales. Violators will be violated.
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Old 10-01-2012, 05:24 PM   #9 (permalink)
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Originally Posted by StJimmy666 View Post
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.
have u brought up with your prof yet? >: )
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Old 10-01-2012, 05:51 PM   #10 (permalink)
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