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 $&gt; 1$. If it is not, then what does this number say to me?

results = load('first_try.mat');
Y = results(:,1);
Y_predicted = results(:,2);

o = sqrt(sum((Y-Y_predicted).^2)/rows(Y))
K-NN is a measure of distance, thus the result of your equation will depend on the scale of your data. If the ratings are in a scale from 0 to 100. Then if you always predict very poorly you are evidently going to have values much larger than 1.

For example, for a very bad predictor

import numpy as np

Y = [100, 90, 100, 90]
Y_p = [10, 10, 10, 10]

np.sqrt(np.sum(np.subtract(Y, Y_p)**2)/len(Y))



  85.14693182963201