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Question
Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from means are 136 and 148 respectively. The sum of product of deviations from respective means is 122. Obtain the regression equation of x on y
Solution
Given, n = 15, `barx` = 25, `bary` = 18,
`sum(x_"i" - barx)^2` = 136, `sum(y_"i" - bary)^2` = 148,
`sum(x_"i" - barx)(y_"i" - bary)` = 122
Now, bxy = `(sum(x_"i" - barx)(y_"i" - bary))/(sum(y_"i" - bary)^2`
= `122/148`
= 0.82
Also, a' = `barx - "b"_(xy) bary`
= 25 – 0.82 × 18
= 25 – 14.76
= 10.24
∴ The regression equation of X on Y is
X = a' + bxyY
∴ X = 10.24 + 0.82Y
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