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State whether the following statement is True or False: Cov(x, x) = Variance of x

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प्रश्न

State whether the following statement is True or False:

Cov(x, x) = Variance of x

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

True

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Properties of Regression Coefficients
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.3: Linear Regression - Q.2

संबंधित प्रश्न

Bring out the inconsistency in the following:

bYX = 2.6 and bXY = `1/2.6`


An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment (₹ y) gave the following results: 

∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6

Estimate the expenditure on food and entertainment when expenditure on accommodation is Rs 200.


From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17


For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.


The equations of two regression lines are x − 4y = 5 and 16y − x = 64. Find means of X and Y. Also, find correlation coefficient between X and Y.


In a partially destroyed record, the following data are available: variance of X = 25, Regression equation of Y on X is 5y − x = 22 and regression equation of X on Y is 64x − 45y = 22 Find

  1. Mean values of X and Y
  2. Standard deviation of Y
  3. Coefficient of correlation between X and Y.

For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.


If bYX = − 0.6 and bXY = − 0.216, then find correlation coefficient between X and Y. Comment on it.


Choose the correct alternative:

If the regression equation X on Y is 3x + 2y = 26, then bxy equal to 


Choose the correct alternative:

If byx < 0 and bxy < 0, then r is ______


Choose the correct alternative:

|byx + bxy| ≥ ______


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 = ______


State whether the following statement is True or False:

If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent


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


Corr(x, x) = 1


The geometric mean of negative regression coefficients is ______


byx is the ______ of regression line of y on x


The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Find the value of the correlation coefficient


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 = 25

Mean of y = 20

`sigma_x` = 4

`sigma_y` = 3

r = 0.5

byx = `square`

bxy = `square`

when x = 10,

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

∴ y = `square`


The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.

  x y
Mean 53 142
Variance 130 165

`sum(x_i - barx)(y_i - bary)` = 1170


|bxy + byz| ≥ ______.


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