Corr(x, x) = 1 - Mathematics and Statistics

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MCQ
True or False

Corr(x, x) = 1

Options

  • True

  • False

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Solution

This statement is True.

Concept: Properties of Regression Coefficients
  Is there an error in this question or solution?
Chapter 2.3: Linear Regression - Q.2

RELATED QUESTIONS

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find Correlation coefficient between X and Y.


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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

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  Sales Adv. Exp.
Mean 40 6
S.D. 10 1.5

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For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0.  The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.


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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.


Regression equations of two series are 2x − y − 15 = 0 and 3x − 4y + 25 = 0. Find `bar x, bar y` and regression coefficients. Also find coefficients of correlation.  [Given `sqrt0.375` = 0.61]


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  X Y
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Choose the correct alternative:

Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σx = 2, σy = 8


Choose the correct alternative:

bxy and byx are ______


Choose the correct alternative:

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


Choose the correct alternative:

If r = 0.5, σx = 3, σy2 = 16, then bxy = ______


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Both the regression coefficients cannot exceed 1


State whether the following statement is True or False: 

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


State whether the following statement is True or False:

Corr(x, x) = 0


If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______


If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______


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Given the following information about the production and demand of a commodity.
Obtain the two regression lines:

  ADVERTISEMENT (x)
(₹ in lakhs)
DEMAND (y)
(₹ in lakhs)
Mean 10 90
Variance 9 144

Coefficient of correlation between x and y is 0.8.
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Given the following information about the production and demand of a commodity.

Obtain the two regression lines:

  Production
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Demand
(Y)
Mean 85 90
Variance 25 36

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If n = 5, Σx = Σy = 20, Σx2 = Σy2 = 90 , Σxy = 76 Find Covariance (x,y) 


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`


If byx > 1 then bxy is _______.


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