Universities use indexes to measure the eligibility of admission candidates. These indexes vary, but they are generally a function of SAT scores and GPA. For University Free for All (UFfA), the admission index (ai) is obtained through

where tsat is the sum of SAT Critical Reading and Math Scores. Download the file “Admissions13” which has 2013 data for 1850 admissions to UFfA. dai is the recorded admission index.
a) Construct a simple linear regression equation to see if gpa explains dai at 5% significance.
b) Construct a 95% confidence interval for the slope of gpa.

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ai = 50gpa + 0.5 3 -(tsat - 400)