हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

Given, bYX = − 0.6, bXY = − 0.216

∴ r = `+-sqrt("b"_"XY" * "b"_"YX")`

`= +- sqrt(- 0.216 * (- 0.6)) = +- sqrt(0.1296)`

∴ r = ± 0.36

Since bXY and bYX are negative,

r is also negative.

∴ r = - 0.36

∴ X and Y negatively correlated.

shaalaa.com
Properties of Regression Coefficients
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Linear Regression - Miscellaneous Exercise 3 [पृष्ठ ५४]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 3 Linear Regression
Miscellaneous Exercise 3 | Q 4.12 | पृष्ठ ५४

संबंधित प्रश्न

For bivariate data. `bar x = 53`, `bar y = 28`, byx = −1.2, bxy = −0.3. Find the correlation coefficient between x and y.


Bring out the inconsistency in the following:

bYX = bXY = 1.50 and r = - 0.9 


Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25


For a certain bivariate data

  X Y
Mean 25 20
S.D. 4 3

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


The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

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

Coefficient of correlation between sales and advertisement expenditure is 0.9.

Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.


In a partially destroyed laboratory record of an analysis of regression data, the following data are legible:

Variance of X = 9
Regression equations:
8x − 10y + 66 = 0
and 40x − 18y = 214.
Find on the basis of above information

  1. The mean values of X and Y.
  2. Correlation coefficient between X and Y.
  3. Standard deviation of Y.

The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find 

  1. Correlation coefficient
  2. `sigma_"X"/sigma_"Y"`

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.

The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
and 20x − 3y − 900 = 0
Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.


Choose the correct alternative:

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


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 = ______


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


|bxy + byx| ≥ ______


The geometric mean of negative regression coefficients is ______


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


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`


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`


bXY . bYX = ______.


If byx > 1 then bxy is _______.


|bxy + byz| ≥ ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×