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$\text { Suppose you were to use PCA on the following dataset }$

(a) On the figure above, draw the line that is in the direction of the first principal component of the data.
(b) Justify your answer to part (a) in one sentence.
(c) One the line below, draw what the dataset will look like after projecting onto the first principal component.
We are not looking for you to make a picture-perfect projection, but your drawing should capture the general idea of how the data will be projected onto the first principal component.

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This is the direction that minimizes reconstruction error (alternatively, the direction of maximum variance).

 

$(c)$ 

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