Question

In: Statistics and Probability

Here is a bivariate data set. x y 70.9 24.2 46 21.3 44.4 20.8 57.6 23.4...

Here is a bivariate data set.

x	y
70.9	24.2
46	21.3
44.4	20.8
57.6	23.4
76.5	25.4
52.3	20

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

Expert Solution

x	y
70.9 46 44.4 57.6 76.5 52.3	24.2 21.3 20.8 23.4 25.4 20

X - M_x

Y - M_y

(X - M_x)²

(Y - M_y)²

(X - M_x)(Y - M_y)

12.950
-11.950
-13.550
-0.350
18.550
-5.650

Mx: 57.950

1.683
-1.217
-1.717
0.883
2.883
-2.517

My: 22.517

167.703
142.802
183.602
0.122
344.103
31.922

Sum: 870.255

2.834
1.480
2.947
0.780
8.314
6.334

Sum: 22.688

21.799
14.539
23.261
-0.309
53.486
14.219

Sum: 126.995

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
∑ = 347.7
Mean = 57.95
∑(X - M_x)² = SS_x = 870.255

Y Values
∑ = 135.1
Mean = 22.517
∑(Y - M_y)² = SS_y = 22.688

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 126.995

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

r = 126.995 / √((870.255)(22.688)) = 0.9038

correlatio coefficient(r) = 0.904

the coefficient of determination(r²) = 0.8169.

which means,

81.7% proportion of the variation in y explained by the variation in the values of x

Thank You...||

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orchestra answered 1 year ago

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