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The regression equation of y on x is 2x – 5y + 60 = 0 Mean of x = 18 2□- 5 y¯+60 = 0 ∴ y¯=□ σx:σy = 3 : 2 ∴ byx = □□ ∴ byx = □□ ∴ r = □

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प्रश्न

The regression equation of y on x is 2x – 5y + 60 = 0

Mean of x = 18

`2 square -  5 bary + 60` = 0

∴ `bary = square`

`sigma_x : sigma_y` = 3 : 2

∴ byx = `square/square`

∴ byx = `square/square`

∴ r = `square`

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उत्तर

The regression equation of y on x is 2x – 5y + 60 = 0.

Mean of x = 18

`2barx -  5bary + 60` = 0

`2 xx 8 - 5bary + 60` = 0

∴ `5 bary` = 36 + 60

∴ `5 bary` = 96

∴ `bary` = 19.2

`sigma_x : sigma_y` = 3 : 2

2x – 5y + 60 = 0 ⇒ y = 0.4x + 12

∴ byx = `2/5`

∴ byx = `("r"sigma_y)/sigma_`

∴ 0.4 = `"r"xx 2/3`

∴ r = `0.4 xx 3/2`

∴ r = 0.6

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Properties of Regression Coefficients
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.3: Linear Regression - Q.5

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Bring out the inconsistency in the following:

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Choose the correct alternative:

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If bxy < 0 and byx < 0 then ‘r’ is > 0


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Obtain the two regression lines:

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Mean 85 90
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For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):

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Mean of x = 53

Mean of y = 28

Regression coefficient of y on x = – 1.2

Regression coefficient of x on y = – 0.3

a. r = `square`

b. When x = 50,

`y - square = square (50 - square)`

∴ y = `square`

c. When y = 25,

`x - square = square (25 - square)`

∴ x = `square`


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`sigma_y` = 3

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byx = `square`

bxy = `square`

when x = 10,

`y - square = square (10 - square)`

∴ y = `square`


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