Understanding linear regression

A simple scenario would be where one would like to predict whether a student is likely to be accepted into a college undergraduate program (such as Princeton University) based on the data of the GPA score and the SAT score with sample data as follows:

In order to be able to consider the acceptance versus some score that is a combination of the SAT score and the GPA score, just for the purposes of illustrating an example here (note that this does not resemble the actual admissions process), we will attempt to figure out the line of separation. As the SAT scores vary from 2100 to 2390 along the x axis, we can try five values from y=2490 – 2*i*2000. In the following example, we have 2150 instead of 2000. GPA along the y axis has extreme values as 3.3 and 5.0; therefore, we use the incremental values starting with 3.3 using 3.3+0.2i from one extreme and 5.0-0.2i from the other extreme (with a step size of 0.2).

As a first attempt to see how the data visually...