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State whether the following statement is True or False: The following data is not consistent: byx + bxy =1.3 and r = 0.75

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Questions

State whether the following statement is True or False:

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

State whether the following statement is True or False:

If byx + bxy = 1.3 and r = 0.75 then the given data is inconsistent.

Options

  • True

  • False

MCQ
True or False
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Solution

This statement is true.

Explanation:

The given data is inconsistent because the equation byx + bxy = 1 + r2 should hold. Here 1 + (0.75)2 = 1.5626, but the given sum is 1.3, which contradicts the formula.

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

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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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x y xy x2 y2
6 9 54 36 81
2 11 22 4 121
10 5 50 100 25
4 8 32 16 64
8 7 `square` 64 49
Total = 30 Total = 40 Total = `square` Total = 220 Total = `square`

bxy = `square/square`

byx = `square/square`

∴ Regression equation of x on y is `square`

∴ Regression equation of y on x is `square`


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