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The dataset comprises bandwidth usage for each customer. There is also a hybrid metric based on the distance covered by each traffic flow and aggregated to obtain 'Bit-Miles' for each customer (sum of traffic $\times$ miles for each flow).

Clearly, there is some (causal) dependence among the above features but owing to skewness I had to resort to transformations (log, square root, z-scores etc.)

After transforming both bandwidth and bit-miles, I see a strong linear relationship.

Does this imply that bit-miles is a redundant feature (which seems counter-intuitive IMHO had there been no transformation)?

Can I somehow prove/disprove that 'Bit-Miles' is redundant?

Here are the plots before and after the transformation. before

after

Here is a small view of the data as well.

Name            Traffic(bps)            Bit-Miles
Customer1       729797243234.54         416983889869721.00
Customer2       411886504711.92         43841920479614.30
Customer3       253240650503.96         269534485841579.00
Customer4       251982742984.49         158900272002478.00
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  • $\begingroup$ Its worth pointing out that the observations are not independent since traffic from each customer is inherently dependent on the traffic from/to another customer. I'm not sure which statistics should make sense in this case. $\endgroup$ – tool.ish Mar 6 '14 at 8:57
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I think "redundant" may be too strong. First, the relationship, while strong, isn't perfect (what is r on the transformed data?) Second, the variable on the y-axis has some features that the one on the x axis does not (a floor effect and a gap).

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  • $\begingroup$ Ahh. I suspected that and wanted to get an expert's opinion. Thank you very much. Notice another feature that there is an almost perfectly linear top boundary on the transformed data? $\endgroup$ – tool.ish Mar 6 '14 at 6:59

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