Consider the following small data set. Subject x y 1 7 23 2 6 31 3 8 29 4 1418 5 6 24 Find the linear correlation coefficient. r:l l A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance' The verbal scores and final grades for all 10 students in the class are shown in the table below. Student Verbal Score 3 Final Grade y 1 67 81 2 50 64 3 58 93 4 26 85 5 38 83 6 47 65 7 45 88 8 58 95 9 59 100 10 33 79 Find the following: (a) The correlation coefficient: 1' :l ' (b) The least squares line: :1} :l ' (c) Calculate the residual for the eighth student' l I Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Empathy Score 40 49 36 56 53 59 60 51 42 44 57 70 25 59 34 107 Brain Activity -0.129 0.3810.006 0.378 0.013 0.407 0.098 0.52 0.148 0.743 0.258 0.567 0.223 0.729 03610.77 I L2 0 a 0 subject 8 o . O I O C 0.1 O I a I 43.4 Given that ttequation for the regression line is g] : 0.007839: 7 0.07021, what is the residual for subject 8? ANSWER: l l