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# Senstivity Analysis Using Output from PROC Reg

Hi All,

I'm relatively a new user and it will be my first question on here.

I've built a Customer Conversion model for a leading retailer in US. The goal is to identify Key Business Drivers of Customer Conversion.

I used SAS Enterprise Miner to build this model. The dataset has about 1200 variables, used LARS as a variable selection technique and then used TRANSFORM node on selected variables to allow both the transformed and raw variables to compete for a final spot in the model (PROC Reg).

The model was finally baked and the variables make intuitive sense.

Furthermore,  I was asked to work on the Sensitivity Analysis on the output of the model. One of the variables(ratio ..e.g. Number of Boxes / worker) has an Inverse transformation which means the more Workers we have for a given box, the higher the response variable is.

As there is cost associated to adding an additional worker, the total benefit is computed as (Predicted_Net_Sales - Worker Cost).

Note: Net_Sales can be predicted easily after Conversion is predicted using the final regression equation.

The goal of this analysis is to find an optimal number of workers such that benefit is maximized.

For example,

Conversion = 9.31

Net Sales = \$100

Cost = 1*15 = \$15

Profit = Net_sales -Cost = \$85

Conversion = 9.35 (using the final equation)

Net_sales = \$123

Cost= 2*15 = \$30

Profit = Net_sales - cost = \$123-\$30 =\$93

Benefit = Scenario 2 - Scenario 1 = \$93-\$85 = \$8

Here is my problem, for sensitivity analysis, the predicted conversion using the final regression equation increases in a linear  fashion when I increase the number of workers (transformed variable) . However, when I remove the transformation for that specific variable,  I get a graph that follows the Law of Diminishing returns, which means that the number of workers can be added to a certain value and beyond that it won't be feasible to add additional workers as the benefits would outweigh the cost incurred in adding workers. I like the transformed version of this variable as it helps bump up the R-Square of the model.

Would it be possible to conduct sensitivity analysis on the transformed variable and reproducing the same graph which mimics Law OF Dimishing returns theory?

Also, I would like to have your valuable suggestions on how to conduct sensitivity analysis based on the output (final variables) of the Regression Model that involves Variable Transformations?

Sorry for keeping this post a bit longer than intended. Please feel free to ask any additional questions.

Thanks,

Akshay

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