Notes

Linear Regression

Problem Formulation

\[ \left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]

Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation. MathJax equations can be used this way without unduly disturbing the spacing between lines.

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This is the first paragraph.

In the ex1/

  1. The data is loaded from housing.data. An extra 1 feature is added to the dataset so that \(\theta_1\) will act as an intercept term in the linear function.

Once you complete the exercise successfully, the resulting plot should look something like the one below:

Example plot produced by the exercise

Yours may look slightly different depending on the random choice of training and testing sets. Typical values for the RMS training and testing error are between 4.5 and 5.