Find Correlation Coefficient from two Regression line equations calculator

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Solution

Solution provided by AtoZmath.com

Method-1 :

1. Find the equation of regression lines and estimate y for x = 1 and x for y =4.

X	3	2	-1	6	4	-2	5	7
Y	5	13	12	-1	2	20	0	-3

Method-2 :

1. The regression equation of two variables are 5y = 9x - 22 and 20x = 9y + 350
Find the means of x and y. Also find the value of r.

Method-3 :

1. The following information is obtained form the results of examination

	Marks in Stats	Marks in Maths
Average	39.5	47.5
S.D.	10.8	16.8

The correlation coefficient between x and y is 0.42. Obtain two regression lines and estimate y for x = 50 and x for y = 30.

Method-4 :

1. The following information is obtained for two variables x and y. Find the regression equations of y on x.

`sum XY` = 3467	`sum X` = 130	`sum X^2` = 2288
n = 10	`sum Y` = 220	`sum Y^2` = 8822

Example (with steps)

1. Find Correlation Coefficient from two Regression line equations X+2Y-5=0, 2X+3Y-8=0

Solution:
`x+2y-5=0`

`:.x+2y=5`

and `2x+3y-8=0`

`:.2x+3y=8`

`x+2y=5 ->(1)`

`2x+3y=8 ->(2)`

equation`(1) xx 2 =>2x+4y=10`

equation`(2) xx 1 =>2x+3y=8`

Substracting `=>y=2`

Putting `y=2` in equation`(1)`, we have

`x+2(2)=5`

`=>x=5-4`

`=>x=1`

`:.x=1" and "y=2`

`:. bar x = 1, bar y = 2`

Suppose `X+2Y-5=0` is regression equation of `y` on `x`

`=>1 x +2 y -5 = 0`

`=>2 y = -1 x +5`

`=>y = (-1)/(2) x +5/(2)`

`=>y = -0.5 x +2.5`

`:. byx = -0.5`

Suppose `2X+3Y-8=0` is regression equation of `x` on `y`

`=> 2 x +3 y -8 = 0`

`=> 2 x = -3 y +8`

`=> x = (-3)/(2) y +8/2`

`=> x = -1.5 y +4`

`:. bxy = -1.5`

`r = sqrt(byx * bxy)`

`=sqrt(-0.5 * -1.5)`

`=sqrt(0.75)`

`=-0.866`