# FAQ: K-Nearest Neighbor Regressor - Weighted Regression

This community-built FAQ covers the “Weighted Regression” exercise from the lesson “K-Nearest Neighbor Regressor”.

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Why is the denominator the sum of 1/each distance?

1 Like

I think it’s something like the weighted average but inversed. I checked several webpages saying that it’s called “Inversed Distance Weighting”. I will use some pseudo-code to explain.

Imaging you’re doing a weighted average for a list of number and their counts, the weighted average should equal to
`numbers = [the list of numbers]`
`counts = [the list of corresponding counts]`
`weighted_average = sum([number * count for (number, count) in zip(numbers, counts)] / sum(counts)`

You could imagine `sum(counts)` as
`sum = 0`
`for count in counts:`
` sum += count`

Now we want to do a inversed weighted average, which means we could convert each count to 1/count. The larger `count`, the smaller `1/count`.

Thus, the denominator becomes `1/count_1 + 1/count_2 + 1/count_3 + ... 1/count_n`

That’s how I understand the inversed weighted average! Hope it could help you.

3 Likes

Thanks! The key idea is to make the weights smaller when the distance is greater, so that’s why we take the inverse of each distance as the weight for each rating. Great explanation!

3 Likes

In exercise 1 we had a score of 6.86. With the weigthed we had a score of 6.849139678439045. The IMDB rating for The incredibles 2 is 7.8. The weighted algorithm actually performed even worse than the original.

Could someone explain us why. Than you.