Distinguishing the influence of two independent variables

[electricpete]

In attached tab summarysheet, I have vibration at 9 different locations on a machine (1A, 1H1, 1H2, 2A…3H2)…. Columns C thru J. Each row represents a different date/time when data was taken as a batch (all points).

In columns L and M are a representative temperature (winding temperature.. fluctuates with ambient temperature) and date of the reading.

ChartWithTemp shows the data – there appears an increasing trend with time, particularly on 1A, 1H2, 2H2. (1H2, 2H2, 3H2 all in the same direction)

The very first point 9/29 was a different fluid system lineup than the rest, and may not be representative.

If we disregard that first point, we see an increasing trend in vibration over time and a decreasing trend in temperature over time.

The important question arises, is vibration changing due to passage or time or due to change in temperature.

I attempted to analyse it with some statistics, but still seems inconclusive:
Tab: TempCorrelation shows results of single linear regression of all vibration points against temperature. R^2 IS 0.79 for 1H2 and 0.76 for 2H2

Tab: TimeCorrelation shows results of single linear regression of all vibration points against time. R^2 IS 0.72 for 1H2 and 0.70 for 2H2

Tab: TimeTempCorrelation shows results of multiple linear regression of the single point 1H2 against two independent variables: time and temperature. R^2 is 0.88. The F statistic (mentioned in another thread) is 52 (number of data points = 17). The slopes for the m1 and m2 parameters are both more than 3 standard deviations… which might suggest neither slope is 0.

What conclusions might reasonably be drawn about the likelihood that the change in vibration is a result of time, temperature, or both?


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[GregLocock]

If I understand it correctly your time and temp ar emore closely correlated (higher R^2) than either time or temp with your other measurements. So really you need more data.

I'd build some sort of simple model

Vib=k1*time+k2*temp+k3

and do a least squares fit for k1 and k2 and k3 using solver.

The proper approach is a principal moments analysis, about which I know nothing.



Cheers

Greg Locock

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[IRstuff]

Data is not the problem nor the issue. When two things are tightly correlated, there is nothing in the data to tell you which is cause and which is effect. That's the realm of the physics model, and completely unrelated to the data.

Consider y = x + 5; it's only by convention that x is the indepedent variable. We could just as easily look at the system as x = y - 5, and every correlation test would be equally valid.

A real-life example is the correlation between smoking and lung cancer. From a pure statistical perspective, the tobacco companies can rightly argue that those that are prone to lung cancer are driven to smoke. Only the biological model of cancer can tell you that the chemicals in the smoke damage the lungs and thereby cause the cancer.

TTFN

FAQ731-376

 

[GregLocock]

I recommend Antaeus for looking at this sort of stuff, as a first look.

My quick model says temp is about twice as important as day, for the ranges given.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

My problem stems from the fact that my two independent variables (time and temperature) are for the moment tightly correlated to each other.

I agree with Greg that more data will help in the following sense: next spring temperatures will start coming up. If vibration continues to climb we know the relevant variable is time. If vibration decreases we'll know the relevant variable is temperature. But I don't want to wait that long....



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[MintJulep]

Can you get some data where the temperature reaches steady state?

If the vibration stays constant then you'll have your answer.

 

[electricpete]

Temperature varies at roughly a constant rise above ambient temperature (with slight lag of one or two hour time constant). Since I don’t control ambient, I take what I get. But I agree again more would be better - Even if we don’t wait for spring in theory I think more data (with bumps up/down in temperature over time) should eventually distinguish between the two variables. At this point the R^2 for the two correlations (vs time and vs temp) don’t seem to have enough spread to draw a conclusion with confidence. What kind of analysis did you do Greg?

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[Latexman]

Do you have access to JMP? It's a much better tool for what you are doing than Excel.

Good luck,
Latexman

 

[GregLocock]

I did what I said I'd do. For the vibration signal I first normalised each by the alert level, and then took the average of all the channels, and ignored the first reading.

Cheers

Greg Locock

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[spciesla]

Why not use the Excel CORREL() function to compare the vibration and temperatures?

Another option is to calculate the average and standard deviation values for each position. If you discard the 09/29/09 data, I don't think any of the measurements exceed 3 standard deviations over the average. It would be diligent to compare against some "sister" components that have similar operating characteristics.

Steve

 

[GregLocock]

Here's a comparison for the model I hashed up.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.