Question

7. A recent major study between High Blood Pressure and Heart determined the Coefficient of Non-Determination was .51   

1. Compute the Person Product Moment Correlation Coefficient

2. Compute the Coefficient of Non-Determination

3. Compute the Coefficient of Non-Determination

n	1	2	3	4	5	6	7
x	11	17	13	12	15	10	12
y	21	20	20	19	18	23	20

(10 points)

X	Y	XY	X2	Y2
11	21	231	121	441
17	20	340	289	400
13	20	260	169	400
12	19	228	144	361
15	18	270	225	324
10	23	230	100	529
12	20	240	144	400
90	141	1,799	1,192	2,855

(Sum of x’s) = 90

(Sum of y’s) = 141

(Sum of x*y) = 1,799

(Sum of x2) = 1,192

(Sum of y2) = 2,855

Sample Size = 7

x = Age at First Contact with the Law

y = Age of Incarceration

Answer 1

Ʃx =	90
Ʃy =	141
Ʃxy =	1799
Ʃx² =	1192
Ʃy² =	2855
Sample size, n =	7
x̅ = Ʃx/n = 90/7 =	12.85714286
y̅ = Ʃy/n = 141/7 =	20.14285714
SSxx = Ʃx² - (Ʃx)²/n = 1192 - (90)²/7 =	34.85714286
SSyy = Ʃy² - (Ʃy)²/n = 2855 - (141)²/7 =	14.85714286
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 1799 - (90)(141)/7 =	-13.8571429

Correlation coefficient, r = SSxy/√(SSxx*SSyy)

= -13.85714/√(34.85714*14.85714) = -0.6089

Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy)

= (-13.85714)²/(34.85714*14.85714) = 0.3708

Coefficient of Non-Determination = 1 - 0.3708 = 0.6292