मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

If u = x-ac and v = y-bd, then bxy = ______

Advertisements
Advertisements

प्रश्न

If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______ 

रिकाम्या जागा भरा
Advertisements

उत्तर

`"c"/"d"` buv 

shaalaa.com
Properties of Regression Coefficients
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.3: Linear Regression - Q.3

संबंधित प्रश्‍न

Bring out the inconsistency in the following:

bYX = 2.6 and bXY = `1/2.6`


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


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.


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
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find 

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

For a bivariate data, `bar x = 53`, `bar y = 28`, byx = −1.5 and bxy = −0.2. Estimate y when x = 50.


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.


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


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.


The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.

  X Y
Mean 50 140
Variance 150 165

and `sum (x_i - bar x)(y_i - bar y) = 1120`. Find the prediction of blood pressure of a man of age 40 years.


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:

|byx + bxy| ≥ ______


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 = ______


Choose the correct alternative:

Both the regression coefficients cannot exceed 1


Corr(x, x) = 1


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


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


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


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 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Find the value of the correlation coefficient `("Given"  sqrt(0.933) = 0.9667)`


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`


The regression equation of y on x is 2x – 5y + 60 = 0

Mean of x = 18

`2 square -  5 bary + 60` = 0

∴ `bary = square`

`sigma_x : sigma_y` = 3 : 2

∴ byx = `square/square`

∴ byx = `square/square`

∴ r = `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 = ______.


For a bivariate data:

`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

Find: 

  1. byx
  2. bxy
  3. Correlation coefficient between x and y.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×