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All righty.

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Now we've covered mean absolute error.

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We're going to have a look at Main squared error here actually and make a little heading as usual because

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we're keeping our notebook nice and clean.

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I mean squared error.

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Wonderful.

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And then we're going to go means squared error.

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Now you might.

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Based off what we've looked at with mean absolute error you might be able to deduce how we might calculate

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means squared error if not again perfectly fine so if we come down here from that skyline dot matrix

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import mean squared error wonderful.

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And so we're going to do it basically in the exact same way.

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So MSE equals mean squared error except this time instead of using absolute we're going to be using

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squared then we're going to take the Y test labels and because we've already made predictions up here

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why spreads.

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We could make them again but we might just reuse values here.

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Why spreads.

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Actually for completeness what we might do is just the Y spreads equals model not predict and we're

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predicting on The X test data because we want to compare our predictions to the Y test data.

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They're going to have look at MSA nine point two for two.

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Mm hmm.

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It's a little bit higher than what we got with mean absolute error.

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Well that's because MSE or main square I should put MSA in here right.

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Because there's so many acronyms these days MSE will always be higher than mean absolute error because

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it squares the errors rather than only taking the absolute difference into account.

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So if we come up here and have a look this data frame would be the exact same here.

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So what mean absolute error does is it takes these values and it turns negatives into positive adds

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them all up and then finds the average over what means squared error does is it takes these values squares

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them then adds them all up and then finds the average hence the main squared error.

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So that's why the squaring part squaring these numbers will lead to a higher number here.

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Actually we might just do it.

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So let's see if we can calculate MSE by hand.

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And this is dangerous right we're going off the record here.

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Calculate MSA by hand.

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So all we have to do is take the differences here so actually def differences we need a square that

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actually might do here.

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So.

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Is it empty square empty askew square dance differences and then should we add a called the main on

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that actually.

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Let's put that in brackets can we do that don't mean right.

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Squared equals that what does squared look like OK.

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So this is going to take this column here and squared now to calculate the MSE.

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We just need to take the main of squared beautiful.

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There we go.

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See that's how we calculate the main squared error.

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That's it right.

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We've covered means quite ere we covered mean absolute error and we covered square.

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Now the next logical question is and even if you aren't asking it is which regression evaluation metric

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should you use.

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So we look here we'll come back to the KEYNOTE so our squared is similar to accuracy right.

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It gives you a quick indication of how well your model might be doing.

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Generally the closer you are squared value or coefficient of determination value is to 1 the better

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the model.

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But as we've seen before us square doesn't really tell us exactly how wrong our model is in terms of

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how far off each prediction is for that mean absolute error gives a better indication of how far off

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each of your model's predictions are on average.

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So that's when we saw this one here.

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Right.

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This is how we saw on average each of our models predictions is about two point one two away from what

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it actually should be.

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Whether that's positive or negative.

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And so we come back here now can get a bit confusing which to use between mean absolute error and mean

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squared error.

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Well because of the way main squared error is calculated.

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We saw that by calculating it by hand.

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We squared the differences and then took the main right instead of just taking the absolute differences

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because of how MSE is calculated squaring the differences between predicted values and actual values.

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It amplifies larger differences.

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So you could imagine if we had a difference of say 10 and we squared that right.

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That's going to be now a difference of 100 and we're taking the average of that.

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So let's say we're predicting the value of houses which we are.

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You want to pay more attention to mean absolute error when being ten thousand dollars off is only twice

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as bad as being 5000 dollars off.

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So that makes sense right.

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But pay attention more to means squared error when being ten thousand dollars off is more than twice

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as bad as being five thousand dollars off.

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You might think well it's not really if I double 5000 dollars to ten thousand dollars.

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So this is kind of another way of saying is that when bigger errors are bigger than smaller errors.

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Right.

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So if we're ten thousand dollars off and that's way worse than being 5000 dollars off we want to look

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more to means squared error.

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Long story short you want to a little tidbit here is for regression models you want to minimize mean

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squared error and minimize mean absolute era while maximizing r squared right.

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So does that make sense.

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Minimize mean absolute error minimize means squared error while maximizing R squared.

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Now that we've covered a handful of some of the most useful in common regression metrics we come back

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here.

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We see that there's still a fair few more that we could have done right.

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So that's a little challenge to you is to dive into model evaluation metrics.

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But the ones we've gone through a more than enough to get started you might be thinking hold on.

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We haven't even used the scoring parameter which is what we talked about five or six videos ago.

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Well now that we've covered some of the as I said some of the most common and useful regression and

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classification metrics we can finally take a look at the scoring parameter which is what we'll do in

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the next couple of videos.