Question

WILL FAN AND MEDAL!
So this is more of a thinking and real-world example problem, but I was wondering how to model data with a linear function, and what real world scenarios use linear data?

Answer 1

If any of you can help, please message me your help. Thanks!

Answer 2

Many real-world scenarios can be adequately modeled with linear functions over carefully chosen intervals. One example that comes up frequently in physics problems is the approximation of \(\sin \theta \approx \theta\) for sufficiently small values of \(\theta\).

Answer 3

Okay, but how can you model data with a linear function. How would you even know it is a function?

Answer 4

This data presumably comes from experimental measurements of some sort. Typically, one does a scatter plot to see if there is any apparent trend in the data, and based on that trend, you do something like a least-squares fit of a line through the data. Real-world data is typically full of "noise" and so rarely will all the data fall exactly on the graph of the modeling function, whatever it is.

Answer 5

For example, here's a scatter plot of some data and a line which fits the data pretty well. How do I know that? Because the data is simply the points on the line with a small random number (both positive and negative values) added to it.

Answer 6

Thanks, that makes a lot of sense. I couldn't quiet understand how to explain it, and that helps.