The Archer Foundation offers summer internships to college s

The Archer Foundation offers summer internships to college students usually following their sophomore year of college. Most of the internships are paid internships in government agencies. It is rumored that the Foundation uses GPA to help determine pay, but they do not have a minimum GPA requirement for being granted an internship. Below are data from a sample of 10 interns showing GPA and Summer Stipend received.

GPA (X)             Stipend (Y)

2.95                     $5,500

3.21                     $4,850

3.30                     $5,700

2.82                     $4,900

3.28                     $5,200

3.60                     $6,500

3.57                     $6,200

3.42                     $6,150

3.87                     $7,000

3.92                     $6,800

Mean GPA = 3.394 with a Standard Deviation of .359

Mean Stipend = $5880 with a Standard Deviation of $768.91

What percent of variation in Stipend can be predicted by using GPA?

Solution

Note that the correlation is

r^2 = [nSum(xy) - Sum(X)Sum(y)]^2 / [(nSum(x^2) - Sum(x)^2)(nSum(y^2) - Sum(y)^2)]

Thus, as n = 10

r^2 = [10(201790.50) - (33.94)(58800)]^2 / [10(116.352) - 33.94^2)(10(351065000) - (58800)^2]

Thus,

r^2 = 0.801087011 = 80.109%

Thus, the percent of variation that can be predicted is 80.109%. [ANSWER]