In: Statistics and Probability
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 10 students are shown in the table below.
Student 1 2 3 4 5 6 7 8 9 10
Score 65 42 32 43 59 73 31 25 74 71
Grade 79 63 85 93 93 79 86 74 67 92
Find the following: (a) The correlation coefficient: r=
(b) The least squares line: y^=
(c) The predicted grade for the eighth student:
(d) The residual for the eighth student:
The statistical software output for this problem is:
Hence,
a) Correlation coefficient (r) = -0.0036
b) Least square line: = 81.2029 - 0.0020x
c) Predicted grade = 81.153
d) Residual = 25 - 81.153 = -56.153