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Regression – Recommendations
In the following screenshot, we can see that visually it looks better (even though
a few outliers may be having a disproportionate impact on the result):
Ideally, though, we would like to measure how good of a fit this is quantitatively.
In order to do so, we can ask how close our prediction is. For this, we now look
at one of those other returned values from the np.linalg.lstsq function, the
second element:
(slope,bias),total_error,_,_ = np.linalg.lstsq(x,y)
rmse = np.sqrt(total_error[0]/len(x))
The np.linalg.lstsq function returns the total squared error. For each element, it
checks the error (the difference between the line and the true value), squares it, and
returns the sum of all these. It is more understandable to measure the average error,
so we divide by the number of elements. Finally, we take the square root and print
out the root mean squared error (RMSE). For the first unbiased regression, we get
an error of 7.6, while adding the bias improves it to 6.6. This means that we can
expect the price to be different from the real price by at the most 13 thousand dollars.
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