Could I use a mean squared error statistical analysis on a set of 1 x 2 matrices? For example, if I had [123 456] as the actual matrix and [111 222] as the predicted matrix, could I use the mean square error to evaluate the accuracy of this model? If this does not work or is not an optimal choice, what else could I use? Thanks
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2$\begingroup$ In fairness a two-dimensional matrix where one of the two dimensions equals to one is usually called a vector. Maybe you overcomplicate things by thinking for matrices. $\endgroup$– usεr11852Commented Oct 22, 2015 at 18:13
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It depends on the nature of the data and problem. If both of these variables matter equally, and they are on the same scale, then using the mean square error is OK.
Different scales could be a problem. For example, if the first variable ranges from 1 - 10000 and the second ranges from 1 - 10, then the error in the first variable could dominate any changes in the error in the second variable.
Since you're only dealing with two variables, you might considering taking the absolute elementwise difference between the predicted and ground truth matrices.
So given your example, it'd be |[123 456] - [111 222]| = [22 234]. Then try to minimize this.
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$\begingroup$ Thanks. I've looked at the frobenius norm also, which seems to provide a similar metric for how close the prediction was to the actual value. But what could I use for these matrices/vectors that would tell me, "Your predictions show x% correlation with the actual data" $\endgroup$ Commented Oct 24, 2015 at 12:49
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$\begingroup$ To be honest, I don't think using this kind of summary statistic makes sense, because it's only 2 values. You could calculate the error as a percentage of the actual value, and say something like, "the prediction is within 20% of the actual value." Maybe someone else has better ideas? $\endgroup$– KarmenCommented Oct 25, 2015 at 20:25