Question

a. Compute the sample covariance. 112.255 (Round to three decimal places as needed.) b. Compute the coefficient of correlation. r= 1.000 (Round to three decimal places as needed.) c. How strong is the relationship between X and Y? Explain. A. The variables X and Y have a perfect negative correlation because all points fall on a straight line with a negative slope. B. The variables X and Y have a perfect positive correlation because all points fall on a straight line with a positive slope. C. The variables X and Y have no correlation.

Answer 1

X	Y
12 30 30 36 28 38 16 12 28 14 6	6 15 15 18 14 19 8 6 14 7 3

X - Mx	Y - My	(X - Mx)2	(Y - My)2	(X - Mx)(Y - My)
-10.727 7.273 7.273 13.273 5.273 15.273 -6.727 -10.727 5.273 -8.727 -16.727 Mx: 22.727	-5.364 3.636 3.636 6.636 2.636 7.636 -3.364 -5.364 2.636 -4.364 -8.364 My: 11.364	115.074 52.893 52.893 176.165 27.802 233.256 45.256 115.074 27.802 76.165 279.802 Sum: 1202.182	28.769 13.223 13.223 44.041 6.950 58.314 11.314 28.769 6.950 19.041 69.950 Sum: 300.545	57.537 26.446 26.446 88.083 13.901 116.628 22.628 57.537 13.901 38.083 139.901 Sum: 601.091

Key

X: X Values
Y: Y Values
M_x: Mean of X Values
M_y: Mean of Y Values
X - M_x & Y - M_y: Deviation scores
(X - M_x)² & (Y - M_y)²: Deviation Squared
(X - M_x)(Y - M_y): Product of Deviation Scores

Result Details & Calculation

X Values
∑ = 250
Mean = 22.727
∑(X - M_x)² = SS_x = 1202.182

Y Values
∑ = 125
Mean = 11.364
∑(Y - M_y)² = SS_y = 300.545

X and Y Combined
N = 11
∑(X - M_x)(Y - M_y) = 601.091

Covarience calculation:

cov(x,y)= ∑(X - M_x)(Y - M_y)/N = 601.091/11 = 54.645

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 601.091 / √((1202.182)(300.545)) = 1

Y Values X Values

The variable X and Y have a perfect positive correlation because all point fall on a straight line with positive slope.

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