Question

Obtain the two regression equations form the following data :
X :
6
2
10
4
8
Y:
9
11
5
8
7

Answer 1

this is the answer of your question hope it's helpful for you

Answer 2

x = -0.95y + 12.65 .

y = – 0.2474 x + 7.4844.

Given:

X :       6    2     10     4     8

Y :       9    11     5      8     7

XY :   54  22  50  32  56

To Find:

The two regression equations form the following data.

Solution:

n = 5

X bar  =  ∑ x / n    =  30/5   = 6

Y bar  =  ∑ y / n    =  40/5   = 8

b xy = ( n  ∑xy -  ∑x .  ∑y ) / n  ∑$y^{2}$ - ( ∑y $)^{2}$

b xy = 5 x  191 - 30 x 35  /  5 x 265 - (35)      ^2

      =  -95/384

       = 0.2474

Regression equation of x on y:

(x – x̄) = bxy (y – ȳ)

x – 6 = -0. 95 (y -7)

= -0.95 y + 6.65

x = -0.95 y + 6.65 + 6

x = -0.95y + 12.65

Regression equation of y on x:

(y – ȳ) = byx (x – x̄)

y – 6 = -0.2474 (x – 6)

= -0.2474 x + 1.4844

y = – 0.2474 x + 1.4844 + 6

y = – 0.2474 x + 7.4844.

Hence the two  regression equations are :

x = -0.95y + 12.65 .

y = – 0.2474 x + 7.4844.

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