= Solution
The one-dimensional <principal component analysis> reconstruction lies along $v_1=(4/5,-3/5)^T$ through the zero <sample mean>. Its discarded <principal component> coordinate is $PC_2=0$, so
$$
\frac35x+\frac45y=0,\qquad y=-\frac34x.
$$
At $x=6$, \b[$\boxed{\widehat y=-4.5}$.] This intersects the retained <principal component> line with the vertical line at the supplied $x$. It is a reconstruction from that line, rather than an ordinary <linear regression> of $y$ on $x$.
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