Linear Regression

Problem Formulation

This can be a link: Lecture Note on Supervised Learning for more.

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

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. As you see, MathJax equations can be used this way as well, 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 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:

(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.