Question

30. For regression 5X + 10Y - 145 = 0 ; 14Y+; 8X - 208 = 0 . The mean values ( overline X , overline Y ) is:
(a)(5, 12)
(b) (12, 5)
(c) (12, 3)
(d) None​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

For regression

5X + 10Y - 145 = 0 ; 14Y + 8X - 208 = 0 .

$\sf{The \: mean \: values \: \: (\bar{X} \: , \: \bar{Y} ) \: \: is}$

(a) (5, 12)

(b) (12, 5)

(c) (12, 3)

(d) None

EVALUATION

Here the given regression equations are

5X + 10Y - 145 = 0 - - - - - - (1)

14Y + 8X - 208 = 0 - - - - - - (2)

Which can be rewritten as

X + 2Y = 29 - - - - - - (1)

4X + 7Y = 104 - - - - - - (2)

$\sf{Let \: the \: mean = ( \bar{X}, \bar{Y}) }$

Then we have from above

$\sf{ \bar{X} + 2 \bar{Y} = 29 \: \: \: \: \: - - - - (3) }$

$\sf{ 4\bar{X} + 7 \bar{Y} = 104 \: \: \: \: \: - - - - (4) }$

Multiplying both sides of Equation 3 by 4 we get

$\sf{ 4\bar{X} + 8 \bar{Y} = 116 \: \: \: \: \: - - - - (5) }$

Equation 5 - Equation 4 gives

$\sf{ \bar{Y} = 12 }$

From Equation 3 we get

$\sf{ \bar{X} = 5 }$

Thus we get

$\sf{\bar{X} = 5 \: , \: \bar{Y} = 12 }$

FINAL ANSWER

Hence the correct option is (a) (5, 12) ━━━━━━━━━━━━━━━━

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