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So the next question is: how well does the model fit to data? Now, as a challenge,
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do you remember how to print out a regression's r-squared value from the previous lessons?
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I want you to print out two different r-squared values.
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I want you to print out the r-squared value for the training dataset and the r-squared value for the
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testing dataset.
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I'll give you a few seconds to pause the video and give this a shot. And here's the solution - to obtain
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the r-squared,
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we access it through the regression object's score method.
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So my first print statement is gonna read
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"'Training data r-squared: ', regr.score(X_train, y_
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train)".
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So this will be the r-squared of the training dataset; and the r-squared of the testing dataset will
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be "'Test data r-squared:', regr.score(X_test, y_
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test)".
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So let's take a look at what these turn out to be.
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For our training data we get an r-squared of 0.75 and for our test dataset we get
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an r-squared of 0.67.
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Now these values are actually both quite high.
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I mean when you think about it, the real world is a very, very complicated place.
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But we've been able to explain approximately 75 percent of the variance in our house prices with just
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13 features. 13 things and we can explain a lot of what's going on in the real world. Now a question that
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you might ask looking at these two values is: why is the r-squared lower for the test dataset?
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And the answer is is that what we've done so far is calculate the thetas only on our training data.
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The algorithm hasn't seen the test data before.
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As such, the performance of our model on the data that a model hasn't seen is always gonna be worse.
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It makes sense for the r-squared to be lower on the test data than on the training data.
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However, running the model on data that's not in the sample actually gives us some idea of its predictive
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power.
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We get a little bit of a feeling for how our model would fare in the real world.
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And it's very encouraging to see that the r-squared even on the test data is still quite high.
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So our model actually performs relatively well.
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Okay, so we spec'd out our model and we've run our first regression.
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We did a quick sense check and looked at the performance.
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Now we're getting to the evaluation stage. Now before we move on to the next lesson,
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let's add another markdown cell above this one here and add the section heading "Multivariable Regression".
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That way we can keep track of what we're doing.
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The other thing I'm going to do is take these two lines of code,
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cut them and paste them down here.
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That way when I hit Shift+Enter we'll be able to see our data frame of coefficients.
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Otherwise the output is hidden by the print statements.
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There we go.
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Now we're ready to move on.
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I'll see you in the next lessons.