The short answer is, yes. What line goes best through the middle of all points that comprise the entirety or just the surface of an airplane or javelin? Draw it; in your head or on a picture. You are looking for and at that solitary line from which every point (of interest, whether you plot them or not) that would contribute to total least (among points) deviation from that line. If you do it by eye, implicitly by common sense, you will approximate (remarkably well) a mathematically calculated result. For that there are formulae which bother the eye and may not make common sense. In similar formalized problems in engineering and science, the scatters still invite a preliminary appraisal by eye, but in those arenas one is supposed to come up with a "test" probability that a line is the line. It goes downhill from there. However, you are apparently trying to teach a machine to size up (in effect) the metes and bounds of (a) a sizeable barnyard and (b) scattered livestock inside it. If you give your machine what amounts to a picture (graphical, algebraic) of the real estate and occupants, it should be able to figure out (midline neatly dividing blob in two, calculated descatter into a line) what you want it to do. Any decent statistics textbook (ask teachers or professors to name more than one) should spell out both the whole point of linear regression in the first place, and how to do it in the simplest cases (ranging to cases that are not simple). A number of pretzels later, you'll have it down pat.
In re: Silverfish's comment to my post supra (there seems no simple way other than this to add comment to that comment), yes, the OP is blind, is learning machine learning, and requested practicality without plots or graphs, but I assume that he is able to distinguish "visualizing" from "vision", visualizes and has veritable pictures in his head, and has a basic idea of all manner of physical in objects the world around him (houses, among others), so he can still "draw" both mathematically as well as otherwise in his head, and can probably put a good semblance of 2D and 3D to paper. A wide array of books and other texts nowadays is available in physical Braille as well as in electronic voice on one's own computer (such as for forums, dictionaries, etc.), and many schools for the blind have fairly complete curricula. Rather than airplane or javelin, sofa or cane would not necessarily be the more appropriate, and statistics texts are probably available. He is less concerned for how machines might learn to plot and graph or calculate regression, then for how machines might learn to do something equivalent (and more basic) in order to grasp regression (whether a machine might display it, react to it, follow it, avoid it, or whatever). The essential thrust (as to blind as well as to sighted students) is still how to visualize what can be non-visual (such as concept of linearity rather than instance of drawn line, since before Euclid and Pythagoras), and how to visualize the basic purpose of a special kind of linearity (regression, whose basic point is best fit to least deviation, since early in mathematics and statistics). A lineprinter's Fortran output of regression is scarcely "visual" till mentally assimilated, but even the basic point of regression is imaginary (a line that isn't there till it is made for a purpose).
