Can I use a dataset even if the observations of a variable are not in the same unit? I am using a dataset where a variable is "height". However, when I read about the construction of the dataset, it seems that some observations in the dataset are labelled in centimetres and others in hectometres, and I don't know which is which, since it is not given in the dataset. (Otherwise I could simple multiply those in hectometres by 10, of course.) Can I still run regressions, even if all the observations of my variables are not in the same unit? Under which conditions?   
 A: 1 hectometer is 10,000 centimeters. So, assuming the same sort of thing is being measured in each observation (whether it's bugs, people, buildings, or mountains), it should be easy to infer which measurements are in which of the two units, by checking if the order of magnitude is reasonable for the thing being measured. For example, a person could be 180 centimeters tall, but not 180 hectometers tall. (Talk about having your head in the clouds, eh? I'll be here all week.)
Without being able to infer the unit, there isn't much you can do, since you can't even tell which two measurements are equal, and when they're not equal, which is bigger. The most you could do is distinguish positive heights from zero heights from negative heights, which is unlikely to be useful because quantities called "heights" are almost always positive.
If each observation has one or more other measurements that are guaranteed to use the same unit, you can at least examine the ratios of these, which are unit-invariant (the units cancel out in the quotients).
A: No. All of your observations must be on the same scale to make mathematical sense of the numbers - there is no "scale" in the model, so "1" can be massively different if one is "1 cm" and the next is "1 hectometer". Without units this data set is worthless.
That said, centimeters and hectometers are massively different, and I urge you to re-evaluate your numbers. 1 hectometer = 100 meters, while centimeters are 1/100 of one meter. Multiplying either by 10 isn't the correct conversion, so I suspect you've misread something.
