English

Choose the correct alternative: |byx + bxy| ≥ ______ - Mathematics and Statistics

Advertisements
Advertisements

Question

Choose the correct alternative:

|byx + bxy| ≥ ______

Options

  • |r|

  • 2|r|

  • r

  • – r

MCQ
Fill in the Blanks
Advertisements

Solution

2|r|

shaalaa.com
Properties of Regression Coefficients
  Is there an error in this question or solution?
Chapter 2.3: Linear Regression - Q.1

RELATED QUESTIONS

Bring out the inconsistency in the following:

bYX = 2.6 and bXY = `1/2.6`


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

  X Y
Mean 85 90
S.D. 5 6

The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.


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.


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.

What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?


For certain bivariate data the following information is available.

  X Y
Mean 13 17
S.D. 3 2

Correlation coefficient between x and y is 0.6. estimate x when y = 15 and estimate y when x = 10.


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.

The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.


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]


The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:

  1. `bar x and bar y`
  2. bYX and bXY
  3. If var (Y) = 36, obtain var (X)
  4. r

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, σy2 = 16, then bxy = ______


Choose the correct alternative:

Both the regression coefficients cannot exceed 1


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


Corr(x, x) = 1


If n = 5, ∑xy = 76, ∑x2 = ∑y2 = 90, ∑x = 20 = ∑y, the covariance = ______


The value of product moment correlation coefficient between x and x is ______


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


byx is the ______ of regression line of y on x


The equations of two lines of regression are 3x + 2y – 26 = 0 and 6x + y – 31 = 0. Find variance of x if variance of y is 36


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


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


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`


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`


If byx > 1 then bxy is _______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×