Consider the follow set of ?=5 (?,?)(x,y) pairs:
?x | 20 | 25 | 26 | 30 | 35 |
?y | 21 | 30 | 35 | 31 | 40 |
NOTE: SXX = 126.8, SXY = 139.6, SYY = 197.2, ?¯x¯ = 27.2, and ?¯y¯ = 31.4.
Compute the sample correlation correct to three decimal places of accuracy.
Correlation = ?=
Answer:
The following table shows the calculations -
x |
y |
x^2 |
y^2 |
xy |
|
20 |
21 |
400 |
441 |
420 |
|
25 |
30 |
625 |
900 |
750 |
|
26 |
35 |
676 |
1225 |
910 |
|
30 |
31 |
900 |
961 |
930 |
|
35 |
40 |
1225 |
1600 |
1400 |
|
Total |
136 |
157 |
3826 |
5127 |
4410 |
Total number of observations, n = 5
Mean of x, = 136/5 = 27.2 (given)
Mean of y, = 157/5 = 31.4 (given)
Sxx = (x^2) - (n x (^2)) = 3826 – (5 x (27.2^2)) = 126.8 (given)
Syy = (y^2) - (n x (^2)) = 5127 – (5 x (31.4^2)) = 197.2 (given)
Sxy = xy - (n x x ) = 4410 – (5 x 27.2 x 31.4) = 139.6 (given)
Therefore, Correlation Coefficient, r = Sxy / (Sxx . Syy)^0.5 = 139.6 / (126.8 x 197.2)^0.5 = 0.883
Consider the follow set of ?=5 (?,?)(x,y) pairs: ?x 20 25 26 30 35 ?y 21...
Problem 1. (16 points) Consider the follow set of n = 5(x, y) pairs: x 2025 26 30 35 y 21 30 35 31 40 NOTE: SXX = 126.8, SXY = 139.6, SYY = 197.2, X = 27.2, and y = 31.4. Compute the sample correlation correct to three decimal places of accuracy. Correlation ==
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