Conditional expectation of errors (residuals) from probit regression

[River Huang]

Dear All, How can I obtain the (conditional) residuals in (3) below (of course, starting from equation (1))?

I have attached a dataset (from my friend) here temp.dta, where the (binary) dependent variable is "cov_h" (similar to cancer in (1) above), along with two explanatory variables "risk_cancer" and "agent". Any suggestions are highly appreciated.

[River Huang]

The first 200 observations are:

* Example generated by -dataex-. For more info, type help dataex
clear
input float cov_h double risk_cancer float agent
1 0 0
1 0 0
0 0 0
1 0 0
0 0 0
1 0 0
1 0 0
0 0 0
0 0 0
0 0 0
1 0 0
0 0 0
1 0 0
1 0 0
1 0 1
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
0 0 0
0 0 1
1 0 0
1 0 0
1 0 0
1 0 0
0 0 0
0 0 1
1 0 0
1 0 0
1 0 0
1 0 0
0 1 0
1 0 0
0 0 1
1 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 0
0 1 1
0 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 0 0
1 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
0 1 0
0 0 0
1 0 0
1 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
0 0 0
1 0 0
1 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
0 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
0 0 0
0 0 0
1 0 0
1 0 0
0 0 0
1 0 0
0 0 0
1 0 0
0 0 0
1 0 0
0 0 0
1 0 0
0 0 0
1 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 1 0
1 0 0
1 0 0
0 0 0
0 0 0
0 1 0
0 0 0
1 0 0
1 0 0
1 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 1
1 0 0
1 0 0
0 0 0
1 0 0
1 0 0
0 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
0 0 0
1 0 0
1 0 0
1 0 0
0 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 0
0 0 0
1 0 0
1 0 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
end