Question

10. The Academic Dean of NCC believes there may be a positive linear relationship between the number of recitations attended by a student during a semester, and the grade received in the course. The following table gives a sample of 12 students' number of recitations attended and their corresponding grades. Student Grade Number of recitations 3 7 Thomas Jose Joe Maria Susan Peter Bella Tyrone Raul Tueta 4 11 13 7 82 90 80 92 90 77 71 68 2 0 5 77 8 0 Nancy Jeff 87 52 84 5 - [2 pts) Determine the coefficient of linear correlation (r) of the given data. [2 pts] Draw a scatter diagram of the given data (Copy from Stat Crunch)

Answer 1

X Y Χ.Υ X.X Υ.Υ 3 82 246 9 6724 7 90 630 49 8100 4 80 16 6400 320 1012 11 121 92 90 13 1170 169 8464 8100 5929 5041 7 77 539 49 2 71 142 4 O 68 O 4624 5 25 5929 77 87 O 385 696 O 8 64 O 52 O 7569 2704 7056 5 84 420 25 Step 2: Find the sum of every column to get: ΣΧ = 65, ΣΥ – 950, ΣΧ. Υ = 5560, ΣΧ? – 531, ΣΥ? - 76640 Step 3: Use the following formula to work out the correlation coefficient. η ΣΧΥ - ΣΧ. ΣΥ T » ΣΧ? - (ΣΣ)?] [ΣΥ (ΣΥ? 12 5560 - 65 - 950 T 0.8183 12 - 531 - 652 - 12 76640 – 9502]