Distinguishing the influence of two independent variables
Distinguishing the influence of two independent variables
(OP)
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?
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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RE: Distinguishing the influence of two independent variables
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
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Distinguishing the influence of two independent variables
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
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RE: Distinguishing the influence of two independent variables
My quick model says temp is about twice as important as day, for the ranges given.
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Distinguishing the influence of two independent variables
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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RE: Distinguishing the influence of two independent variables
If the vibration stays constant then you'll have your answer.
RE: Distinguishing the influence of two independent variables
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RE: Distinguishing the influence of two independent variables
Good luck,
Latexman
RE: Distinguishing the influence of two independent variables
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Distinguishing the influence of two independent variables
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
RE: Distinguishing the influence of two independent variables
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.