math120 ch992f root mean squared error
Sorry that my video in the lower-right covered up the Residuals. Here's the Desmos link where you can see what the residuals are: https://www.desmos.com/calculator/szx...
Sometimes we want to summarize a bunch of numbers down to just 1 number, so we can compare it to something else, or try to make it small, or large. Here is a good way of doing that, in some cases: Mean Squared Error (MSE), or even better, Root Mean Squared Error, RMSE. In some stats classes you might talk about Sum of Squared Errors, which is basically the same idea as Mean Squared error, but SSE = n*MSE, where n is the number of data points. It's much easier to interpret RMSE than MSE or SSE, though. Also, RMSE is very related to Standard Deviation. A difference is that Standard Deviation is, roughly, how far the data points are from the mean, while RMSE is how far the data points are from some particular target, which could be the mean but isn't always--it's up to you, in the context of the application.
Here’s an extra thought about the trendline/RMSE situation: there’s a difference between the prediction system (the idea of using a line, and adjusting the slope and intercept) and the way we measure how good the predictions are (RMSE, for example). We could use RMSE even if we had a nonlinear prediction system. We could use something like Mean Absolute Error (or Mean Absolute Deviation) instead of RMSE whether we use a linear or nonlinear prediction system.
We consider a 1-dimensional version of this problem in this video: • math120 ch31g homework help min sum square...