Find the equation of two regression lines, also estimate 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 Regression line equations from the following data
Class-X Y
2 - 4 3
4 - 6 4
6 - 8 2
8 - 10 1

Solution:

Class-X	Mid value `x`	`y`	`x^2`	`y^2`	*`xy`**
2 - 4	3	3	9	9	9
4 - 6	5	4	25	16	20
6 - 8	7	2	49	4	14
8 - 10	9	1	81	1	9
---	---	---	---	---	---
	`sum x=24`	`sum y=10`	`sum x^2=164`	`sum y^2=30`	`sum xy=52`

Mean `bar x = (sum x)/n`

`=24/4`

`=6`

Mean `bar y = (sum y)/n`

`=10/4`

`=2.5`

`byx = (n sum xy - (sum x)(sum y))/(n sum x^2 - (sum x)^2)`

`=(4 * 52 - 24 * 10 )/(4 * 164 - (24)^2)`

`=(208 - 240 )/(656 - 576)`

`=-32/80`

`=-0.4`

Regression Line y on x
`y - bar y = byx (x - bar x)`

`y - 2.5 = -0.4 (x - 6)`

`y - 2.5 = -0.4 x + 2.4`

`y = -0.4 x + 2.4 + 2.5`

`y = -0.4 x + 4.9`

`bxy = (n sum xy - (sum x)(sum y))/(n sum y^2 - (sum y)^2)`

`=(4 * 52 - 24 * 10 )/(4 * 30 - (10)^2)`

`=(208 - 240 )/(120 - 100)`

`=-32/20`

`=-1.6`

Regression Line x on y
`x - bar x = bxy (y - bar y)`

`x - 6 = -1.6 (y - 2.5)`

`x - 6 = -1.6 y + 4`

`x = -1.6 y + 4 + 6`

`x = -1.6 y + 10`