Here's an easy one to conceptualize: A good friend of mine is a state hydrologist. He crawls over streams with a ladder-like platform and at increments lowers

Here's an easy one to conceptualize: A good friend of mine is a state hydrologist. He crawls over streams with a ladder-like platform and at increments lowers a depth gauge to eventually estimate the stream's volume flow rate. For a number of reasons (including wild weather conditions) the cross stream increment is known only to an inch or so, that's the uncertainty in X, the depth gauge reading has another uncertainty in Y. These are applied to a function where the slope, via Deming regression, gives him an estimate of the flow rate. By the bye, most lab thermometers i've dealt with have an accuracy of about 0.1°C