how could you use a line graph to help you make predictions about data that were not actually measured?

Question

science

Answer 1

GREAT question. This is one of the deepest problems in science and philosophy. It is sometimes referred to as the "riddle of induction." The more general version of your question is, "How do we ever generalize from data?" Hypotheses (or lines in graphs) make infinitely many claims, or predictions, and yet we only ever have finitely many data. So how do we ever become confident in hypotheses?

The short answer is that there is still no great answer. Most supposed answers actually rely on certain assumptions (sometimes "prior probabilities") about things, and once you assume these (or believe in the probabilities of hypotheses prior to having data), you can derive the probability of a hypothesis once you have the data. The problem is that all these rely on assumptions about the data, assumptions not given by the data themselves.

Anyway, take a look at "riddle of induction" or "problem of induction" searches on the internet. Well-known, well-studied problem, and yet not really much progress on it.

Answer 2

There are two ways; one is called extrapolation (extra means going beyond) and the other is called interpolation (inter means going between).

We extrapolate by extending the line formed by the last few points in the graph. If we can identify a trend, we can say, "It has been getting steadily hotter for the last several days. It is safe to predict that tomorrow it will either get a little hotter, remain about as hot as it is now, or get slightly cooler." In other words, we do not expect huge changes in a short time.


We interpolate by drawing a line connecting two dots within the graph. "We took measurements Saturday and Monday, but not Sunday. Looking at the recorded measurements for those two days, however, we can safely say that the temperature Sunday was between the temperatures recorded on Saturday and Monday."

In other words, they are two types of estimates, very useful ones.

Answer 3

You assume that the unmeasured data points are along the same line as the measured data points and thereby interpolate the results not measured mathematically.

Answer 4

It is deliberate ignorance as displayed by some of the answers here. these dupes think they are supposed to walk outside theirs door and notice a .2 degree increase per decade in the temperature. Guys, you must have some very sensitive receptors in your skin. I wonder if the sand is any warmer three feet below the surface where their heads are buried.

Answer 5

Its called extrapolation. Its accuracy it relative to context.