Question

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 1010 students in the class are shown in the table below.

Student	Verbal Score ?x	Final Grade ?y
11	4747	100100
22	7777	7272
33	5353	6262
44	3434	8080
55	5151	7878
66	3939	6767
77	7272	9090
88	5353	8989
99	6161	9999
1010	3535	6868

Find the following:

(a) The correlation coefficient: ?=r=

(b) The least squares line: ?̂ =y^=

(c) Calculate the residual for the tenth student:

Answer 1

The statistical software output for this problem is :

r = 0.2457

y hat = 68.6190 + 0.2276 x

residual = 68 - 76.5852 = -8.5852