How to find the value of two independent variables that make the dependent variable is minimum

[Terrencefung]

Hi SAS community members,

I am trying to find out the values of two independent variables that make the value of dependent variable is minimum.

For example, here is my equation: EC= q1(x1)c1+q2(x2)c2

what i want to do is find out the values of x1 and x2 that make EC is the minimum.

Could anyone please help me for this .

Many thanks for your help.

Regards,

Terrence

[Shmuel]

1) please post a smaple of your data for test.

2) how many observationsare in your dataset ?

3) have you tried to create a sas code ? If yes - post it.

[Terrencefung]

Hi Shmuel,

Thank you very much for your prompt response. Some variables of the equation are known,

The sample data as follow:

Global Company	em	Estimated Probability
Key
1173	1	0.01095
1173	1	0.00952
1286	1	0.00804
3362	1	0.0161
3734	0	0.00812
3839	1	0.0123
3946	1	0.01109
4060	0	0.00972
4060	1	0.01077
4372	1	0.00967
4601	1	0.00978
4601	0	0.00981
4622	1	0.00922
4769	1	0.01033
5047	1	0.01023
5399	1	0.00945
6136	1	0.01154
6136	1	0.00984
6882	1	0.00917
7652	1	0.00949
7652	0	0.00958
7991	1	0.01051
8092	1	0.01075
8972	0	0.01
9538	1	0.01213
10026	1	0.00946

em=1means the observations is a manipulator, 0 otherwise,  Estimated Probability is the estmated probabilty calculated by a Logit model.

 I need to find a cut-off value for Estimated Probability that make EC has the minimum value

EC= q1(x1)c1+q2(x2)c2

where q1=0.01, c1=1 , q2=0.99, c2=20

x1 is the observed Type I error, x2 is the observed the Type II error.

I have 10,000 observations.

Thank you again for your reply.

Kind regards,

Terrence 

[PGStats]

Are q1 and q2 continuous functions? If so, can you find their derivative?

Do you have a licence for SAS/OR?

[Terrencefung]

Hi PG STATS,

Thank you for your reply.

q1 and q2 are assumed probabilities, and not continuous. For example, here i assume the assuemd probabilty for manipulator q1=0.01 (1%), and the assumend probabilty for non-manipulator is q2=0.99 (99%).

Yes, I have the licence for SAS/OR.

Thank you for your help.