It is assumed that achievement test scores should be correlated with student's classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizzes, etc.) would also perform well on a standardized achievement test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she computes a correlation between the students achievement test scores (x) and the overall G. P.A. (y) for each student computed over the entire year. The data for her class are provided below. Achievement(X) G. P.A.(Y)
98 3.6
96 2.7
94 3.1
88 4.0
91 3.2
77 3.0
86 3.8
71 2.6
59 3.0
63 2.2
84 1.7
79 3.1
75 2.6
72 2.9
86 2.4
85 3.4
71 2.8
93 3.7
90 3.2
62 1.6
Estimate β0 and β1. Then, write down the equation of the least squares line.
Find a 90% confidence interval for β1