Find Regression line equations using mean, standard deviation and correlation calculator

SolutionHelp

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

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

1. Find Regression line equations from x = 39.5, y = 47.5, 6x = 10.8, 6y = 15, r = 0.42

Solution:

$byx = r * (sigma y)/(sigma x)$

$byx = 0.42 * 15/10.8$

$byx = 0.58$

Regression Line y on x

$y - bar y = byx (x - bar x)$

$y - 47.5 = 0.58 (x - 39.5)$

$y - 47.5 = 0.58 x - 23.04$

$y = 0.58 x - 23.04 + 47.5$

$y = 0.58 x + 24.46$

$bxy = r * (sigma x)/(sigma y)$

$bxy = 0.42 * 10.8/15$

$bxy = 0.3$

Regression Line x on y

$x - bar x = bxy (y - bar y)$

$x - 39.5 = 0.3 (y - 47.5)$

$x - 39.5 = 0.3 y - 14.36$

$x = 0.3 y - 14.36 + 39.5$

$x = 0.3 y + 25.14$