Suppose we have a linear regression:
Y = mx + b
where X is the independent variable of interest, in this case "scoops of ice cream per order" at an ice cream shop, b is the error term, and Y is the dependent variable of interest, "service time per order" at an ice cream shop. The goal is to find "m", the time it takes to scoop ice cream.
Incoming orders are treated as random, at least for the sake of this argument/question. An order could be for any number of scoops of ice cream. There are also "random" events that happen during the course of an order, for example, like when there is a miscommunication between a guest and a worker about what flavor ice cream they want. When the wrong flavor of ice cream is delivered, the worker will have to take the time to correct the mistake, and this is reflected in the data. There is no correlation between scoops ordered and mistakes like that. However, the mistakes only ever add time to order processing. They never reduce time of order processing.
My question is, it seems that not including the variable "mistakes" will not fit the definition of an omitted variable for the purposes of "omitted variable bias". There is no correlation between scoops and mistakes. However, since I am looking for the mistake-free time it takes to generate one scoop, will my "m" not be shifted upward relative to the theoretical "mistake-free" line? Is there not then some kind of bias here? How could that be corrected?
