Choose the correct alternative: Both the regression coefficients cannot exceed 1 - Mathematics and Statistics

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MCQ
True or False

Choose the correct alternative:

Both the regression coefficients cannot exceed 1

Options

  • True

  • False

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Solution

True

Concept: Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.2

RELATED QUESTIONS

Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25


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bYX = 2.6 and bXY = `1/2.6`


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  X Y
Mean 25 20
S.D. 4 3

And r = 0.5. Estimate y when x = 10 and estimate x when y = 16


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8x − 10y + 66 = 0
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For a bivariate data: `bar x = 53, bar y = 28,` bYX = - 1.5 and bXY = - 0.2. Estimate Y when X = 50.


If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find

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4y − 15x + 500 = 0
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Find the line of regression of X on Y for the following data:

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If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______


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Choose the correct alternative:

bxy and byx are ______


Choose the correct alternative:

If r = 0.5, σx = 3, `σ_"y"^2` = 16, then byx = ______


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The following data is not consistent: byx + bxy =1.3 and r = 0.75


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Given the following information about the production and demand of a commodity.

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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):

  X Y
Mean 13 17
Standard Deviation 3 2

If r = 0.6, Estimate x when y = 16 and y when x = 10


x y `x - barx` `y - bary` `(x - barx)(y - bary)` `(x - barx)^2` `(y - bary)^2`
1 5 – 2 – 4 8 4 16
2 7 – 1 – 2 `square` 1 4
3 9 0 0 0 0 0
4 11 1 2 2 4 4
5 13 2 4 8 1 16
Total = 15 Total = 45 Total = 0 Total = 0 Total = `square` Total = 10 Total = 40

Mean of x = `barx = square`

Mean of y = `bary = square`

bxy = `square/square`

byx = `square/square`

Regression equation of x on y is `(x - barx) = "b"_(xy)  (y - bary)`

∴ Regression equation x on y is `square`

Regression equation of y on x is `(y - bary) = "b"_(yx)  (x - barx)`

∴ Regression equation of y on x is `square`


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`


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`


bxy . byx = ______.


If byx > 1 then bxy is _______.


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