Science:Math Exam Resources/Courses/MATH102/December 2015/Question 05/Hint 1

You can probably identify the line that best fits the data just by looking, but it is better to justify your intuition with a calculation.
The least-squares line is the one that minimizes the sum of the squares of the differences in y-values between the points and the line.
For example, consider picture (a). This picture contains 5 data points: (1,4), (2,3), (3,2), (4,1), and (5,3). The line passes through the points (1,3), (2,3), (3,3), (4,3), and (5,3). The differences in the y-values for these points are -1, 0, 1, 2, and 0. We square each of these numbers to arrive at 1, 0, 1, 4, 0, and add to get 6.
Try performing the same calculation for the remaining 3 lines and figure out which one will minimize this quantity.