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I have an existing algorithm that computes class membership based on how people respond to 25 questions. Answers to each question are multiplied by a regression coefficient (specific to each question), and that total sum classifies into 1 of 6 classes. I am interested in having participants answer the 25 questions then automatically (either in the survey or afterward in an email) receive a notification of their membership. How might I go about doing this? Disclaimer: I am fluent in R and proficient in Python, but don't know any other languages.

You can simply create embedded data in Qualtrics and use math operation to add/sub/mul the coefficients to the embedded and calculate the value for each of them.
Here is the link to get started with math operation.
Math Operations


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