Problem with calculating error rate for KNN

I am trying to validate the accuracy of my KNN algorithm for the movie rating prediction.

I have $$2$$ vectors: $$Y$$ - with the real ratings, $$Y'$$ - with predicted ones.

When I calculate Standard Error of the Estimate (is it the one I need to calculate?) using following formula:

$$\sigma_{est} = \sqrt{\frac{\sum (Y-Y')^2}{N}}$$

I'm getting result of $$\sim 1.03$$. But I thought that it can't be $$> 1$$. If it is not, then what does this number say to me?

Y = results(:,1);
Y_predicted = results(:,2);

o = sqrt(sum((Y-Y_predicted).^2)/rows(Y))
• Why did you think it can't be bigger than 1? Oct 2 '18 at 6:54
• I thought that 1 means that 100% match Oct 2 '18 at 6:54
• That's not what a standard error (SE) is, the SE is the standard deviation (SD) of your estimate, which goes from 0 to infinity. Oct 2 '18 at 6:55
• Depends what you mean by accuracy, the mean is usually used as your accuracy measure, the SE is used to show how variable this measure is (for ex. building a 95 % CI). Whether 1.03 is big in your case depends entirely on your data. Oct 2 '18 at 7:10
• "I thought that 1 means that 100% match" if we had a perfect match (i.e. $Y=Y'$), then wouldn't the numerator of your expression equal $0$ and hence give you $\sigma_{est}=0$? Oct 2 '18 at 8:30