Correlation Coefficient r and Coefficient of Determination

Correlation, Coefficient of Determination

1. Given the following N's (where N is the number of pairs of observations) and obtained r's, indicate whether the result is significant at the .05 level:

(a) N = 100, r = .22
(b) N = 100, r = .60
(c) N = 9, r = -.70
(d) N = 36, r = .23
(e) N = 100, r = -.19

2. Given the following data, what are the correlation and the coefficient of determination between:
(a) IQ scores and anxiety test scores?
(b) IQ scores and statistics exam scores?
(c) Anxiety test scores and statistics exam scores?

Indicate whether the obtained r is statistically significant, and, if so, at what level. Also, would you consider the magnitude of the relationship large enough to be useful in making predictions about student achievement?

Student IQ (X) Anxiety (Y) Statistics Exam Scores (Z)

1 140 14 42
2 130 20 44
3 120 29 35
4 119 6 30
5 115 20 23
6 114 27 27
7 114 29 25
8 113 30 20
9 112 35 16
10 111 40 12

3. Here's another set of measurements; again, find the value of r, whether that value is significant at the .05 level, and the coefficient of determination for each possible pair.

Name Height (inches) Weight (pounds) Shoe Size Ring Size
George 72 200 12 8
Herman 70 160 10 6
Alfie 68 170 11 7.5
Brent 70 150 8 ½ 6.5
Donald 66 150 8 6
Kareem 72 185 11 7 ¾
Graham 66 135 7 ½ 6
Chaco 69 165 9 7.5

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Please see attachment for complete set of questions.

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