# Regression with variables in different scale (how to encode properly and what regression to use?)

I'm working here on my research proposal for my alma mattera. I'm in accountancy science field, however, I need to deal with some statistics on this occassion. Would be very grateful if you could help me.

I have an idea to built this kind of regression model:

Y= x1 + x2 + x3

The research question is: Do audit prices, non audit services provided for audit client and auditor's tenure has an impact on audit quality?

Observation - financial reporting of particular company. Let's say, we have 40 companies and their audited financial reporting.

Y (proxy for audit quality) - count of errors in financial reporting. I guess it would suitable to group the errors found in each observation. For instance, range from 1 to 5 (where 1 - from 0 to 2 errors, 2 - from 2 to 4... and so on.). Or it could be left in relative scale - just how many errors (mistakes in financial reporting) I will found.

x1 - price of audit services of financial reporting. It could be left in model in a relative scale, or coded as 1 - price above the average price in the sample, 0 - price bellow the average price in the sample

x2 - non-audit services provided for the audit client. 1 - there were other services provided, 0 - there where no other services provided.

x3 - the tenure of auditors. Like: 1 - the same auditors are auditing the financial reporting 3 or more years in the row, 0 - the same auditors are not auditing the financial reporting more or equal 3 years. Or it could be put in the model in relative scale: 2, 3, 4, 5, ...8 years in a row.

That's my assumptions how to encode the data. Could you express your opinion how the data should be encoded actually, what kind of regression should I use here and what statistical tests would be suitable for evaluating the results?

Thank you very much