There's lots of research into this, and it's not that simple.
In fact, there is even research into how people overestimate how simple it is!
Much of the research into the illiptical machine read-outs is aimed at improving the models, so they are more accurate, (or, as we see below, selecting the best models, so they are the ones you see in gyms) so we might predict that old machines would be less accurate than new ones.
In 2013, the US Navy looked into this for their training: *Accuracy of Calories Expended on 7 Commercially Available Exercise Machines:
Validation for use a Cardio Alternatives for the Navy Physical Readiness Test
They found the accuracy depended on the amount of exercise:
In this diagram, the blue line is the ideal, and each of the other lines refers to a machine they tried. Anything to the left of the blue line is the machine underestimating. Anything to the right is an overestimate.
In a 2014 experiment, TESTING THE ACCURACY OF THE CALORIE TRACKER ON ELLIPTICALS, the experimenters only looked at one machine, and concluded "the calorie tracker on the Nautilus ellipticals are not an accurate form of calorie tracking for workouts." Reading between the lines, the elliptical trainer tended to overestimate, but this is not part of their conclusions, so should be treated with caution.
In a 2015 experiment, Do Elliptical Trainers Accurately Estimate Energy Expenditure?, undergraduates compared two machines, and found one was 2.7% underestimating and the other was 24.7% overestimating.
This 2015 paper, The relationship between body fat
percentage and difference in caloric
expenditure as measured by indirect
calorimetry and estimated by an
elliptical trainer is interesting further reading. It describes an experiment that failed to confirm some of the hypotheses, but its introduction covers a lot of interesting aspects the problem - that elliptical machines may be good for weight loss regimes, that their perceived exertion is lower than than might be expected. That the calorie readings are generally considered overestimates. That BMI levels may be important in getting accurate readings.
- I haven't shown that most elliptical machines overestimate by 42%. It isn't that simple.
- I haven't shown that elliptical machines are the worst in accuracy.
In this way, I haven't directly answered the question. However,
- Yes, elliptical readers tend to over-estimate.
- Their accuracy differs between brands.
- Their accuracy differs on the amount exercised.
- Their accuracy may depend on body fat percentages.
- There's a lot more to this, and there's plenty of interesting research.