Question

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?

Answer 1

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`