Data space. Drag a point to move it. right-click or double-click empty space adds a point. Delete a point by double-clicking it, by hovering it and pressing delete, or with its × in Objects. Every x and y in Objects can be typed. Drag a square handle on the line to pivot it, or the line itself to slide it.
Parameter space. The mouse only moves the view: drag to pan the flat map, drag to orbit the height map, shift-drag to pan it, scroll to zoom. On the flat map, drag or scroll over an axis's numbers to stretch that axis alone. The w and b sliders and the line are what move the point.
ℝ³ (exactly three points). Each data point is an axis, so the three y values are one point, and every line is one point ŷ on the plane. Drag to orbit, scroll to zoom, double-click for the default view. Grab ŷ to slide it along the plane: the line moves with it.