In AP Statistics, I often utilized the Least Squares method to find correlations between two data sets. First, I would generate a curve that minimized the residuals: the differences between corresponding values of the two sets. Smaller residuals implied greater correlation, with a residual of r = 0 being optimal. The process works as long as the data analyzed is a random sample from the two sets.
I will now perform Least Squares reduction, juxtaposing my traits and expectations for college with my impression of Stanford. Consider the data points below.
Californian: On a scale from 1 to 10, with 10 representing the CA stereotype, I am a 9. I value the environment, I have an enviable tan, and my casual dress belies my assiduous personality. Stanford (a 10) is undoubtedly Californian due to its association with Silicon Valley and John Steinbeck. The resulting residual is r = 1. I belong in CA, and so does Stanford.
Academic Balance: I excel at math and science; I enjoy writing and the arts. Stanford fosters the perfect balance of innovation and imagination. r = 0.
Opportunity: I’d be delighted to explore the plethora of research and job opportunities at Stanford and in the Bay Area. r = 0.
Distance: San Diego is 32N. Stanford is 37N. r = 5, close enough for me!
Climate: San Fran is San Diego minus the Santa Anas. r = 0.
Numeration: Stanford is currently number 1 on my list of colleges. I would love to be 1 more active student on campus. r = 0.
The residuals are sufficiently small, implying a strong correlation!
Normally, I’d do some number crunching at this point to find the exact correlation. However, since I have not yet experienced Stanford, I cannot guarantee the randomness of the aforementioned data. To determine the true correlation, I first require a Stanford education.