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Question
For bivariate data. `bar x = 53`, `bar y = 28`, byx = −1.2, bxy = −0.3. Find the correlation coefficient between x and y.
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Solution
Given:
`bar x = 53`,
`bar y = 28`,
byx = −1.2,
bxy = −0.3.
Correlation coefficient between x and y:
r = `+-sqrt("b"_"xy" * "b"_"yx")`
`= +- sqrt((-0.3)(-1.2))`
= `+- sqrt 0.36`
= ± 0.6 ...[∵ byx and bxy are negative]
Since byx and bxy both are negative,
r is also negative.
∴ r = −0.6
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Mean of x = 53
Mean of y = 28
Regression coefficient of y on x = – 1.2
Regression coefficient of x on y = – 0.3
a. r = `square`
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`y - square = square (50 - square)`
∴ y = `square`
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`x - square = square (25 - square)`
∴ x = `square`
Mean of x = 25
Mean of y = 20
`sigma_x` = 4
`sigma_y` = 3
r = 0.5
byx = `square`
bxy = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `square`
The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.
| x | y | |
| Mean | 53 | 142 |
| Variance | 130 | 165 |
`sum(x_i - barx)(y_i - bary)` = 1170
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