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February 1st, 2016, 07:29 AM   #1
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Multivariable Regression(with factors) Help

Hi All,

I am looking to run a regression analysis on a time study. The study recorded the time it took to service the client, the services provided (could be multiple for the same client), and the size of the client. Larger clients will take longer to service but there are economies of scale per se. A client twice as large will not take twice as long to service. In my regression, I want to solve for the coefficients but also the "size factor" coefficients.

Other notes:
Client 's were grouped into 3 bands based on size: "Small, Medium, & Large"
There are three different services. Can be chosen in any combination. Think al a carte

Y= time (in FTE's)

b1 = service 1
b2 = service 2
b3 = service 3

s1 = small client factor
s2 = medium client factor
s2 = large client factor

X and Z are dummy variables.

Desired output:
Y = (b1*X1 + b2*X2 + b3*X3) * (s1*Z1 + s2*Z2 + s3*Z3)

The idea is that time is a factor of size and service, in contrast to <time = Service 1 + Service 2 + Large Client> which would be the output in a "normal" regression.

I'm looking for ideas on how to solve this problem. I really appreciate the help. Please let me know if I need to provide more detail

Thanks,
Bill
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