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I'd like to know the effect of fluctuation of data within certain period of time. Can I use standard deviation of collected data within the period as independent variable to do a regression analysis?

i.e. I counted the number of customers visited and their waiting time every hour for several days. My hypothesis is if the fluctuation of hourly visiting customer census is getting larger, that day the customers will wait longer. If it's possible to use standard deviation as fluctuation measures, do you know any articles which studied in similar way?

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    $\begingroup$ Is this what people study under the name queuing theory? Perhaps some of the answers in the queuing tag may help you. $\endgroup$ – mdewey Aug 8 '17 at 15:03
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My hypothesis is if the fluctuation of hourly visiting customer census is getting larger, that day the customers will wait longer.

I agree that your hypothesis is sound, as long as I can assume that you are talking about the mean wait for the customers.

This makes sense as, if each customer takes 1 minute to serve, then a queue of 10 customers will takes 1 + 2 + 3 ... + 9 = 45 minutes in total. If they came in 2 minutes apart, each customer coming in individually would be served instantly, i.e 0 minutes in total. This 'fluctuation' as you describe would be caused by a higher standard deviation in the time between customers entering the queue.

You may find that, if each customer takes 1 minute to serve, then customers consistently entering 10 minutes apart will have the same mean as customer entering between 5 and 30 minutes apart, even though the SD will be wildly different. Perhaps you could disregard some of these 'extreme', yet not anomalous, values.

Anyway, you could create a set of data points for each day with X as the daily mean waiting time, and Y as the daily standard deviation of the waiting time, and calculate the Product Moment Correlation Coefficient. You should see a strong positive correlation if your hypothesis is correct.

Saying this, would the statistics even be valuable? It's almost common sense that customers entering together would increase wait time. And even if you come to a conclusion, what can you do with that information? You can't go outside and tell customers to come back later. Perhaps you should compare queue size to the amount of time it takes to serve a customer, and see if the problem is there?

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