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प्रश्न
From the data of 20 pairs of observations on X and Y, following results are obtained.
`barx` = 199, `bary` = 94,
`sum(x_i - barx)^2` = 1200, `sum(y_i - bary)^2` = 300,
`sum(x_i - bar x)(y_i - bar y)` = –250
Find:
- The line of regression of Y on X.
- The line of regression of X on Y.
- Correlation coefficient between X and Y.
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उत्तर
Given, n = 20, `barx` = 199, `bary` = 94,
`sum(x_i - barx)^2` = 1200, `sum(y_i - bary)^2` = 300,
`sum(x_i - bar x)(y_i - bar y)` = –250
(i) `b_(yx) = (sum (x_i - barx)(y_i - bary))/(sum(x_i - barx)^2)`
= `(-250)/1200`
= `(-5)/24`
∴ The regression equation of Y on X is
`(y - bary) = b_(yx) (x - bar x)`
∴ (y – 94) = `(-5)/24`(x – 199)
∴ 24Y – 2256 = –5x + 995
∴ 5x + 24y = 3251
(ii) `b_(xy) = (sum (x_i - barx)(y_i - bary))/(sum(y_i - bary)^2)`
= `(- 250)/300`
= `(-5)/6`
∴ The regression equation of X on Y is
`(x - barx) = b_(xy) (y - bar y)`
∴ (x – 199) =`(-5)/6` (y – 94)
∴ 6x – 1194 = –5y + 470
∴ 6x + 5y = 1664
(iii) r = `+-sqrt(b_(yx).b_(xy)`
`= +-sqrt((- 5/24)(- 5/6))`
= `+- sqrt(25/144)`
= `+- 5/12`
Since byx and bxy both are negative,
r is also negative.
∴ r = `(-5)/12`
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