The accompanying data are a subset of data from the report “Great Jobs, Great Lives” (Gallup-Purdue Index2015 Report, gallup.com/reports/197144/gallup-purdue-index-report-2015.aspx, retrieved April 22, 2017). The values are approximate values read from a scatterplot. Students at a number of universities were asked if they agreed that their education was worth the cost. One variable in the table is the percentage of students at the university who responded strongly agree. The other variable in the table is the U.S. News and World Report ranking of the university.

Ranking .......................... Percentage of Alumni Who Strongly Agree
28 ......................................................... 53
29 ......................................................... 58
30 ......................................................... 62
37 ......................................................... 55
45 ......................................................... 54
47 ......................................................... 62
52 ......................................................... 55
54 ......................................................... 62
57 ......................................................... 70
60 ......................................................... 58
65 ......................................................... 66
66 ......................................................... 55
72 ......................................................... 65
75 ......................................................... 57
82 ......................................................... 67
88 ......................................................... 59
98 ......................................................... 75

a. What is the value of r² for this data set? Write a sentence interpreting this value in context.

b. What is the value of s_e for this data set? Write a sentence interpreting this value in context.

c. Is the linear relationship between percentage of alumni who think their education was worth the cost and university ranking positive or negative? Is it weak, moderate, or strong? Justify your answer.