Given the following data, determine the correlation between IQ scores and psycho
ID: 3133874 • Letter: G
Question
Given the following data, determine the correlation between IQ scores and psychology exam scores, between IQ scores and statistics exam scores, and between psychology exam scores and statistics exam scores.
Student
IQ Score
Psychology Exam Score
Statistics Exam Score
1
140
48
47
2
98
35
32
3
105
36
38
4
120
43
40
5
119
30
40
6
114
45
43
7
102
37
33
8
112
44
47
9
111
38
46
10
116
46
44
Calculate the coefficient of determination for each of these correlation coefficients, and explain what it means. In addition, calculate the regression equation for each pair of variables.
Student
IQ Score
Psychology Exam Score
Statistics Exam Score
1
140
48
47
2
98
35
32
3
105
36
38
4
120
43
40
5
119
30
40
6
114
45
43
7
102
37
33
8
112
44
47
9
111
38
46
10
116
46
44
Explanation / Answer
FOR IQ SCORE (x) AND PSYCHOLOGY EXAM SCORE (y):
Using technology, we get
slope = 0.274369986
intercept = 9.004132566
Thus, the regression line is
y^ = 0.274369986 x + 9.004132566
Also, getting the correlation,
r = 0.553172898
Thus, the coefficient of determination is
r^2 = 0.306000255
Hence, 30.6% of the variation in psychology exam scores are explain by the variation in IQ scores.
********************************
FOR IQ SCORES (x) AND STATISTICS EXAM SCORES (y):
Using technology, we get
slope = 0.316830079
intercept = 4.976420063
Thus, the regression line is
y^ = 0.316830079 x + 4.976420063
Also, getting the correlation,
r = 0.682434168
Thus, the coefficient of determination is
r^2 = 0.465716394
Hence, 46.57% of the variation in statistics scores is explained by the variation in IQ scores.
**********************************
FOR PSYCHOLOGY EXAM SCORES (x) AND STATISTICS EXAM SCORES (y):
Using technology, we get
slope = 0.58629776
intercept = 17.43083004
Thus, the regression line is
y^ = 0.58629776 x + 17.43083004
Also, getting the correlation,
r = 0.62636618
Thus, the coefficient of determination is
r^2 = 0.392334591
Hence, 39.23% of the variation in statistics exam scores is explained by the variation in psychology exam scores.
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