Best fitting line

• Vector $\mathbf v$ (move this by dragging the head of the arrow; click here to optimize)
• Orthoprojector is $P = \frac1{\|\mathbf v\|^2} \mathbf v \mathbf v^{\scriptscriptstyle\mathsf{T}}$
• Data points $\mathbf a_1,\dotsc, \mathbf a_m$ (move by dragging the points; click here to re-randomize)
• Projections of data points $P\mathbf a_1,\dotsc,P\mathbf a_m$ (automatically computed)
• Cost (sum of squared distances to line) is 9.384528147037937

Please excuse the horrible Javascript and user interface design.