1. Do a little research in the library or on the Internet and find out how the least squares method came about, and in what ways it has been used.

Answer this question with a lively little survey of Gauss and Lagendre using it in astronomy, almost a hundred years before the correlation coefficient was devised by Pearson and Galton. Also deal with the question of the intimate relationship between regression and linear algebra/matrix algebra and the relatively late development of that branch of mathematics (1858 or so). Refer to the fun little mathematics history website by Oliver Knill at Harvard. Schlomo Sternberg, Jacques Philippe Marie Binet, etc.

http://www.math.harvard.edu/~knill/history/matrix/index.html