I have a dataset of ~2000 entries (for example, model of car).
For each car model I know the weight of the car, and the power output. I don't know the price or age, which is likely to affect the power to weight ratio of the car. I have a reasonable amount of faith in the data, but some manufacturers might fib a bit (maybe 5% of the data is unreliable).
How can I determine, in a defensible way, the best power output for a given weight of car?
I'm mathematically literate to an engineering undergraduate level, but don't have any statistics experience beyond high school.
I've thought of the following:
- Sort cars by power/weight ratio and then take the top n%. Problem is the determination of n.
- Graph the data and plot a trendline through it. This will underestimate the best power output by a large factor.
- Take the best power to weight ratio and just use that. Problem is that power to weight ratios do not necessarily scale linearly with car weight (it may be easier to produce a small car with a high power to weight ratio for example).
- Bin the data into weight categories, then do the same as above. Problem is that taking a single datapoint from an unreliable dataset doesn't seem right.
- As above, but trying to cross-check the data against outside information (for example, magazine performance tests). This information isn't available for all cars, so probably unfeasible.
For my curiosity, what is the name of these class of problems? It seems like something that would occur commonly, but I don't know how to search for it. Is there an English to Statistics translation tool somewhere?