You can get the graphs to look more similar by modeling the '1' response instead of the '0' response:
proc logistic data = in_data plots=effect;
model binary_variable(event='1') = continuous_variable ;
run;
However, the REGRESSIONPLOT statement performs linear least-square regression, not logistic regression. Thus, you will never completely duplicate the plot by using the raw data.
You can reproduce the plot by using the predicted values from PROC LOGISTIC. For example, the following example uses the OUTPUT statement to write the predicted values to a SAS data set and then plots the results:
proc logistic data = in_data plots=effect;
model binary_variable(event='1') = continuous_variable ;
output out=LogiOut Pred=Pred;
run;
proc sort data=LogiOut;
by continuous_variable;
run;
proc sgplot data=LogiOut;
scatter x=continuous_variable y=binary_variable;
series x=continuous_variable y=Pred;
run;
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