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Colin Jaffe/3 min read

Accuracy Scores in Linear Regression Models

Regression Performance Metrics

R²

Coefficient of determination — 1.0 perfect, 0 = no better than mean.

MAE

Mean Absolute Error — average absolute prediction error.

RMSE

Root Mean Squared Error — penalizes large errors more.

MAPE

Mean Absolute Percentage Error — interpretable as a % deviation.

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Evaluate model accuracy using the score method, comparing predictions to the mean baseline. Watch this tutorial to learn the key concepts and techniques.

Let's find out exactly how accurate our predictions were. So this time what we're going to do is we're going to use the dot score method. Every one of these models has a dot score method that tells you what is the accuracy score.

Now the score method will use different measurements depending on what you're doing. With a linear regression, we get an accuracy score. We'll talk about what accuracy is in a second.

We can say score equals model.score(). And what we give it is the X-test and the Y-test. Now we're giving it the answer and saying, how'd you do? How do your predictions from running X-test data through the model compare to those from the Y-test, the actual answers? And now we can print out the score.

And it's not bad. It's actually very good. It's about 69%.

So what does that mean? It doesn't mean that 69% of them were correct. And that's important to know because, realistically, I bet 0% were exactly correct. Because we're talking about continuous values, which means that nailing it to the decimal point would be very difficult—would be very rare. So it certainly doesn't mean that.

So what is this 69% measuring? It's measuring how close our predictions were, our model's predictions, to a model that just predicted the mean. It just said, listen, look at all these values here, average them out, and guess that each time, right? So just really eyeballing this, we can, actually, we can get the mean. That's pretty easy.

We can say Y-test—it's a list. We can say add up all the Y-test values and divide it by how many Y-test values there are. That's the mean.

So 29.47. If our model just guessed 29.47 for every single one of these, it's just like, yeah, they're all around there. What's this one? 29.47. "Oh, what do you predict given this set of features?" 29.47. It just guessed that for every single one. If it did that, then each one of these, their score would be zero, because it's comparing predictions against that average.

It's no better or worse than just guessing the mean. It's actually possible to have a negative percent here. And what that means is your model performs worse than just guessing the mean every time.

But we're not there. In fact, we're far better than that. We're about 69% better than this.

69% more accurate than just guessing the mean every time. And that's actually really good. That's a very good score.

So next we'll talk about how to make that better.