A couple of simple questions, I hope

1) I'm testing to get a model with average cost of a production unit
as the DV and 15 predictors, the main one being units of a production,
as possible primary IV's. However, the average cost is not very well
correlated with the run size of the job, and in fact other IV's (like
weight, labor cost, machine hours, etc) do a better job. But I assume
I need to use production units as part of the model to establish a
fixed cost of starting the run ?

2) Can I mix,  with any common sense, continuous and categorical IV's  in a model ?

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Request for Question Clarification by maniac-ga on 31 Aug 2005 18:25 PDT

Hello Existential12,

Could you clarify a couple parts of your question?

Can I assume that the "production unit" you are trying to predict the
cost of varies from job to job?

Can you explain if the "labor cost", "machine hours", and other
independent variables are per production unit or for the total
production run? If they vary, please say so (or put into the three
categories I identify below).

Based on the clarification, the answer can be made more specific to
your situation. I will briefly outline the answer as an interim step.

[1] There is no clear relationship between the number of production
units and the "fixed cost of starting the run". There is a
relationship between the number of production units and the total cost
- but only to the extent it affects "variable" costs. I can certainly
go into that in more detail as part of the second part of the answer.

[2] The total cost is most likely made up of the following types of cost:
 - fixed costs (what you would spend if you produced products or not)
 - set up costs (what you spend between to set up each production run)
 - per unit product costs (what you spend to produce a single unit
once the facility is set up)
There are certainly other ways to categorize costs, but from what you
describe this is a good starting point. Depending on how you account
for the costs, the average cost per production unit is made up of some
or all of these types of cost.

After your clarification, I will expand on both parts of the answer
and provide several references that you should find helpful in
refining a final solution for your situation.

  --Maniac

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Clarification of Question by existential12-ga on 01 Sep 2005 06:49 PDT

Thanks, maybe I didn't expand enough. In this example, I have average
cost of the unit (for a job run ranging from 2000 to 10,000 units) ,
which I am comparing to the units in the run. So, you can see that
probably as the run size goes up, average cost decreases. Fit Y by X
on these two shows weak correlation.  Yes, all the other variables are
per unit produced in the run( so machine hours are 2 hours per unit in
the run of say, 5,000). I think I have the answer to my question 2 -
categorical factors can be added.

But the overall problem is the weak correlation (F-test p-value is
.72) between av cost and units (log units actually, this is more
linear) even when factoring in the other variables, which do a good
job of explaining the variance. My overal R-square is about 0.71, so
is it a problem the the primary IV , units (in the run) is
"insignificant".  Let me post the results here, that may help:


Source	  Nparm	       DF        SS 	F Ratio	         Prob > F
Log units	1	1 	0.83287	  0.1217	0        0.7276
goal_sd	1	1	1       136.90141 20.0045	  <.0001
Material Cost	1	1	507.0052  74.0852         <.0001
manager		4	4        134.0520 4.8970	          0.0009
factory	 1	1	1        770.731	  112.6216	  <.0001
labor_hrs	1	1	364.42845 53.2514	  <.0001
stoppages	1	1	133.03252 19.4391	  <.0001

Thanks in advance

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Request for Question Clarification by maniac-ga on 01 Sep 2005 18:42 PDT

Hello Existential12,

Based on what you describe, I believe the results you see are to be
expected. I did a simple example in Microsoft Excel that seems to have
similar results.

Column A - Job size, values in A2 to A11 from 1000 to 10000 in increments of 1000
Column B = Cost, 1100, 2100, ... 10100 in B2 to B11 in increments of
1000 (cost is 100 + job size * 1)
Column C = Cost per Unit, =B2/B1 in cell C2, and fill down, you should
get values 1.1, 1.05, ... 1.01.

Select a range of cells two columns wide and five rows tall. Enter the formula
  =LINEST(B2:B11,A2:A11,,TRUE)
when you "enter" the formula, make sure you hold the control key down
(or command key on a Macintosh) to make this an 'array formula".
Search excel help for "enter an array formula" if you want more
information on how this works. You should get a result like the
following:
1	100
0	0
1	0
#NUM!	8
82500000	0
R squared is one (as expected). The excel help for LINEST lists the
factors in each cell.

Now select another two column by five row region and enter
  =LINEST(C2:C11,A2:A11,,TRUE)
In this case the result is
-7.40524E-06	1.070018519
1.90483E-06	0.011819133
0.653883518	0.017301439
15.11360604	8
0.004524104	0.002394718
and the R squared value is 0.653 which is pretty close to your 0.71.

Does your data show similar results (run size is a good predictor of
total cost but a poor predictor of average cost)?

Another thing to try is to plot the average cost (Y) by number of
production units (X). With this sample data, the plot is not linear,
it drops dramatically at the left and flattens off on the right side.

Let me know if this provides the insight you need [and if not, how the
example does not fit your situation].

  --Maniac

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Clarification of Question by existential12-ga on 16 Sep 2005 05:22 PDT

Thanks for your replies. Actually, I got a reaosnable fit in the end
by using some interactions.

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Request for Question Clarification by maniac-ga on 17 Sep 2005 08:38 PDT

Hello Existential12,

If you no longer want an answer, I suggest you close the question. [so
you don't get charged for an answer]

If you want me to write up the discussion more clearly as an answer,
please make another question clarification and I would be glad to do
so.

  --Maniac