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प्रश्न
By using the data `bar"x"` = 25 , `bar"y" = 30 ; "b"_"yx" = 1.6` and `"b"_"xy" = 0.4` find,
(a) The regression equation y on x.
(b) What is the most likely value of y when x = 60?
(c) What is the coefficient of correlation between x and y?
उत्तर
Here, given values are :
`bar"x"` = 25 , `bar"y" = 30 ; "b"_"yx" = 1.6` and `"b"_"xy" = 0.4`
(a) Regression equation y on x is given as :
`"y" - bar"y" = "b"_"yx" ("x" - bar"x")`
`"y" - 30 = 1.6 ("x" - 25)`
`"y" - 30 = 16/10 ("x" - 25)`
5y - 150 = 8x - 200
8x - 5y - 50 = 0
(b) put x = 60 in eq.(i), we obtain
8(60) - 5y - 50 = 0
5y = 480 - 50
5y = 430
y= 86
(c) Coefficient of correlation between x and y
r = `sqrt("b"_"yx" xx "b"_"xy")`
`= sqrt(1.6 xx 0.4)`
`= sqrt(0.64) = 0.8`
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