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PhiNotPi's avatar

How do I "solve" this system of equations when there is random variability involved?

Asked by PhiNotPi (12388 points ) January 30th, 2013

I have a set of data that needs to be analysed. I’ll explain…

Let A and B represent the two unknown inputs to a function. Let X, Y, and Z represent the three known outputs. On the data table, each row is one trial, and the three columns are the three outputs.

Here are my best guesses behind the underlying relationship between the inputs and outputs, based on the original context.
A + B ≈ X
A + f*B ≈ Y
d*A + e*f*B ≈ Z

(X, Y, Z) are known.
(A, B, d, e, f) are unknown.
(A, B, X, Y, Z) change between trials.
(d, e, f) are almost the same between trials, and I want to find the mean values of these constants.

One important detail is that the above is an approximation. There is variability in the outputs. Simply solving a system of equations doesn’t help me, because the points won’t be perfectly on a curve.

So, how would I find the average values of the unknown constants?

To provide some background info, this data is taken from Fluther website weekly traffic data. X is people, Y is visits, Z is pageviews, A is nonmembers, B is members, all in multiples of 1000.

Observing members: 0 Composing members: 0

6 Answers

njnyjobs's avatar

If X, Y and Z are known, providing the values would probably help get approximate answers.

PhiNotPi's avatar

@njnyjobs The values are in my link, and it contains 14 trials of data.

njnyjobs's avatar

are the values of X, Y & Z on your data table a product of your mind? . . . there doesn’t seem to be a commonality in the sets of values.

PhiNotPi's avatar

@njnyjobs No, they aren’t the product of my mind. I edited in a short explanation in the question, but here is a longer explanation for the real source for the data.

This is the original website. This data is based on the weekly, global (the default graph is daily in the US only), traffic data for

X is the number of people each week.
Y is the number of visits each week.
Z is the number of pageviews each week.

A is the number of nonmembers that visit in a week.
B is the number of members that visit in a week.

d is the average number of pages a nonmember views each time he visits the site
e is the average number of pages a member views each time he visits the site

f is the average number of times that a member visits Fluther each week. For nonmembers, this is assumed to be about 1.

glacial's avatar

In the simplest case, I suppose this would have to be multiple regression. If you’re not familiar with statistics, you may have a lot of work cut out for you in terms of making sure your data meet the assumptions of your test, then figuring out what alternatives to try if they don’t.

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