What is the straight line that comes closest to the point on a scatter plot called?

Answer 1

The line that comes closest can go through the point and so it is simply a line through the point. Given one or two points you can always draw a straight line that goes through them.

The issue becomes more interesting when you have three or more points. You need to make some assumptions regarding the shape of the line: is it a straight line, a quadratic curve, an exponential growth or decay, something else.

Next you need to decide what measure you wish to minimise: the absolute vertical distances between the line and the points, the absolute horizontal distances or the absolute perpendicular distances. Or would you rather work with squared distances? Each one of these choices will give rise to a different line and the line that minimises the chosen measure may not pass through a single point.

So, a line that comes closest to the point may not be a particularly "good" line. A "good" line is called a "line of best fit". The most popular measure for minimising is the square of the vertical distance between the line and the point and the resulting line is called the "least squares regression line".