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

State whether the following statement is True or False: If byx = 1.5 and bxy = 13 then r = 12, the given data is consistent - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
Advertisements

उत्तर

False

shaalaa.com
Properties of Regression Coefficients
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.3: Linear Regression - Q.2

संबंधित प्रश्‍न

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.


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


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.


Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on 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.

Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.


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.


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:

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


Choose the correct alternative:

Both the regression coefficients cannot exceed 1


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


State whether the following statement is True or False:

Regression coefficient of x on y is the slope of regression line of x on y


Arithmetic mean of positive values of regression coefficients is greater than or equal to ______


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


Given the following information about the production and demand of a commodity.

Obtain the two regression lines:

  Production
(X)
Demand
(Y)
Mean 85 90
Variance 25 36

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


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`


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`


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×