Question
In: Statistics and Probability
A study was conducted to determine whether the final grade of a student in an introductory...
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 xx | Final Grade yy |
| 11 | 4242 | 8282 |
| 22 | 2626 | 7575 |
| 33 | 4747 | 7171 |
| 44 | 7272 | 7373 |
| 55 | 6565 | 9494 |
| 66 | 3737 | 7676 |
| 77 | 7777 | 9999 |
| 88 | 6060 | 6565 |
| 99 | 6262 | 7979 |
| 1010 | 7474 | 9393 |
Find the following:
(a) The correlation coefficient: r=r=
(b) The least squares line: y^=y^=
(c) Calculate the residual for the tenth student:
Solutions
Expert Solution
Answer a)
The correlation coefficient: r = 0.4940
Answer b)
The least squares line: y = 62.773 + 0.319*x
Answer c)
At x = 74, we get:
y = 62.773 + 0.319*74
y = 86.379
Residual = Observed value - Predicted value
Residual = 93 - 86.379
Residual = 6.621
orchestra answered 1 year agoRelated Solutions
A study was conducted to determine whether the final grade of a student in an introductory...
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
10 students are shown in the table below. Student 1 2 3 4 5 6 7 8 9
10 Score 75 43 37 53 64 62 43 64 75 55 Grade 81 85 98 71 64 65...
A study was conducted to determine whether the final grade of a student in an introductory...
A study was conducted to determine whether the final grade of a
student in an introductory psychology course, x, is linearly
related to his or her performance on the verbal ability test
administered before college entrance, y. The verbal scores and
final grades for 1010 students are shown in the table below.
Student
Verbal Score
Final Grade
1
64
76
2
50
56
3
34
43
4
38
49
5
49
59
6
56
70
7
57
68
8
72...
A study was conducted to determine whether the final grade of a student in an introductory...
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 ?x
Final Grade ?y
11
3636
9090
22
7474
8484
33
4848
8686
44
7474
6868
55
8080
7676
66
2828
9191
77...
A study was conducted to determine whether the final grade of a student in an introductory...
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 researchers hypothesized the linear
model y=β0+β1xy=β0+β1x, where xx is the score on the verbal ability
test and yy is the final grade in the psychology course. The verbal
scores and final grades for students are shown in the table
below.
Student
1
2
3...
A study was conducted to determine whether the final grade of a student in an introductory...
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
1010 students are shown in the table below.
Student
Verbal Score xx
Final Grade yy
1
43
87
2
60
67
3
29
77
4
73
100
5
52
88
6
26
89
7
47
73
8
44...
A study was conducted to determine whether the final grade of a student in an introductory...
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 / Verbal Score x / Final Grade
y
1 / 42 / 88
2 / 68 / 65
3 / 31 / 83
4 / 68 / 64
5...
A study was conducted to determine whether the final grade of a student in an introductory...
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...
A study was conducted to determine whether the final grade of a student in an introductory...
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
1010 students are shown in the table below.
Student
Verbal Score xx
Final Grade yy
11
6565
7878
22
5151
5858
33
6161
7474
44
4949
6161
55
3131
3434
66
6969
8282
77
4747
5252
88
7575...
A study was conducted to determine whether the final grade of a student in an introductory...
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 xx
Final Grade yy
11
3131
9595
22
5959
8585
33
2828
8181
44
4646
7979
55
5151
6464
66
3232
8181
77...
A study was conducted to determine whether the final grade of a student in an introductory...
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
Verbal Score xx
Final Grade yy
1
35
91
2
64
74
3
46
61
4
35
98
5
79
95
6
53
88
7
63
83
8
54...
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