I've got a question regarding call centers. They often have 'average speed to answer' contracts with their clients. Some of them simply require the average to be 60 seconds or under. However, that would simply be too easy. Many of them will do a 90% of calls must be 60 seconds or under. I am trying to come up with some equation/regression/etc to equate the x% under x seconds. Ive got a listing of about 50 observations (monthly totals, speed to answer for every call).

How would I go about setting up a regression like this? What type of regression?

The variables I have to work with are: average speed to answer, percentage of calls that are under the average speed to answer, and the second mark that 70/75/80/85/90/95% of the calls are at (e.g. for an average speed to answer of 60 seconds, the 95% percentile is about 3.5 minutes).

Ideas? Help? Etc? Thanks!

2/22/2010 3:11:56 PM

http://en.wikipedia.org/wiki/Normal_distribution

2/22/2010 3:44:44 PM

That would be fine if there was some normal dist. I have to account for different 'client' environments. Everyone has a different average speed to answer, everyone takes a different number of calls -- the model must account for these. It's not just a simple distribution question.

2/22/2010 3:49:51 PM

^^ Why do you assume the distribution is Normal?

Make a frequency distribution of your data and then make a histogram. See if the data is approximately normal. If it is, then simply find the average and standard deviation of your data and then answer the questions you need answered using a Standard Normal Distribution table.


[Edited on February 22, 2010 at 3:51 PM. Reason : ]

2/22/2010 3:51:09 PM

That would be fine but my samples range from 1,000 to 10,000 calls (depending on client).

The distribution is extremely heavy on the left (very: l\ shaped).

The call volume itself makes a big difference on the shape, so it will need to be some kind of multiple regression. Do I just got with some kind of:

% of calls under Average speed to answer = Bo + B1 (Calls presented) + B2 (ASA)

Then I could just solve for the different percents as they relate to call volumes and ASA? I need the values 70%-99% solved for (i.e. 70% of the calls answered are under x seconds to 99% of the calls answered are under x seconds -- with it accounting for the different distribution present in the model which are driven but the calls offered typically).

2/22/2010 3:58:42 PM

I'm not sure what you're trying to do here. Do you get some refund if less than 90% of their response times are longer than a minute or are you more concerned with seeing if their response time is plausibly less than one minute? If it's the former, just see if 90% of the response times were less than a minute. If it's the latter a simple t-test will suffice.

H0 = Response time >= 1 minute
Ha = Response time < 1

This will tell you if tell you if the average response time is plausibly less than one minute. You could then construct a confidence interval to or any other measure of spread to examine the claims being made.

[Edited on February 22, 2010 at 5:51 PM. Reason : .]

2/22/2010 5:45:22 PM

Step 1: Get the time per call data.
Step 2: Plot a histogram so that you have information about the most basic nature of your distribution.
Step 3: Compute some basic descriptive statistics. e.g. mean, media, mode(s), range, percentages, skewness, kurtosis, etc... Note: not all descriptive statistics are meaningful for all types of distributions. i.e. A mean doesn't tell you much for a bi-modal distribution.
Step 4: Construct some scatter plots of call time vs time-to-answer to see if there is even a correlation or the potential for a non-linear regression.

The data you have isn't very helpful and is insufficient to derive any sort of regression. At best, you may be able to use the percentage values to reconstruct a histogram so you could at least see what the distribution of call times was.

2/22/2010 6:33:45 PM

pm me the data and the questions that you want answered and I'll tell you whats up

2/23/2010 3:48:56 PM

Quote :

"H0 = Response time >= 1 minute Ha = Response time < 1"

This. Use 90% CI and it should take you all of 2 minutes

2/23/2010 3:59:15 PM