# How to compare observed and expected outcomes for continuous data

I am working on some data, more specifically some predictions of some outcomes. The predictions vary on the continuous scale, between $-3$ and $3$. They can for example be:

$x_1=-2.4, x_2=-2.1, x_3=1.4, x_4=0.4, \cdots, x_n=-1.2$

Now, for each prediction, I also have the corresponding results,

$y_1, y_2, \cdots , y_n$,

which also are continuous.

How can I check if my predictions are good or not? I do not have any knowledge whatsoever on how the predictions are made, thus cannot create any confidence interval around the predictions.

However, there is a simple but important twist: the reference or ideal situation here is agreement, i.e. $y = x$, not the more general linear relationship $y = a + bx$. So, correlation can't quite be the answer to your question. For example, $y = x + 100$ and $y = 10x$ would both give correlations of 1 but additive or multiplicative bias in your predictions would presumably not be acceptable.
• By additive bias I mean predicted = observed $+$ constant and by multiplicative bias I mean predicted = observed $\times$ constant. Mar 3, 2014 at 11:31