Find Regression line equations from sum x, sum y, sum x^2, sum y^2, sum xy, n 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

4. Find Regression line equations from ∑x = 130, ∑y = 220, ∑x² = 2288, ∑y² = 8822, ∑xy = 3467, n = 10

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

`=130/10`

`=13`

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

`=220/10`

`=22`

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

`=(10 * 3467 - 130 * 220 )/(10 * 2288 - (130)^2)`

`=(34670 - 28600 )/(22880 - 16900)`

`=6070/5980`

`=1.02`

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

`y - 22 = 1.02 (x - 13)`

`y - 22 = 1.02 x - 13.2`

`y = 1.02 x - 13.2 + 22`

`y = 1.02 x + 8.8`

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

`=(10 * 3467 - 130 * 220 )/(10 * 8822 - (220)^2)`

`=(34670 - 28600 )/(88220 - 48400)`

`=6070/39820`

`=0.15`

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

`x - 13 = 0.15 (y - 22)`

`x - 13 = 0.15 y - 3.35`

`x = 0.15 y - 3.35 + 13`

`x = 0.15 y + 9.65`