Let us say a number of workers work on 3 products P1, P2 and P3. We measure the workers' performance by time to complete a product. Let us say P1 takes on average 10 hours to complete, P2 30 hours and P3 100 hours. Let us say the averages are medians and the distributions are not symmetric and have different dispersions. How can one assess each workers performance w.r.t. these averages? A simple idea is to use linear regression with this formula:
Time = Bias/P1 + alpha * P2 + beta * P3
Here P1 is the reference and P2 + P3 the dummies based on the original data:
WorkerId Product Time 1 P1 10 1 P2 30 2 P1 15 ...
workedid P2 P3 Time 1 0 0 10 1 1 0 30 2 0 0 15
Could one simply assess the performance of each worker by their average (arithmetic mean?) residuals by applying each worker to the fitted model or is there more to it? Do I have to center/transform/log the variables?
I guess heteroscedasticity is violated due to each product following differeent distributions. Should I rather use quantile regression or a machine learning model? Please note that this is a simplified scenario and products have properties, which on could add to the model.