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

Choose the correct alternative: If r = 0.5, σx = 3, σyσy2 = 16, then byx = ______

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

If r = 0.5, σx = 3, `σ_"y"^2` = 16, then byx = ______

पर्याय

  • 0.375

  • 0.667

  • 2.667

  • 0.093

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

0.667

shaalaa.com
Properties of Regression Coefficients
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.3: Linear Regression - Q.1

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.


You are given the following information about advertising expenditure and sales.

  Advertisement expenditure
(₹ in lakh) (X)
Sales (₹ in lakh) (Y)
Arithmetic Mean 10 90
Standard Mean 3 12

Correlation coefficient between X and Y is 0.8

  1. Obtain the two regression equations.
  2. What is the likely sales when the advertising budget is ₹ 15 lakh?
  3. What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

Bring out the inconsistency in the following:

bYX + bXY = 1.30 and r = 0.75 


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.


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.


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.


If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find

  1. `bar x`,
  2. `bar y`,
  3. bYX
  4. bXY
  5. r [Given `sqrt0.375` = 0.61]

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:

Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σx = 2, σy = 8


Choose the correct alternative:

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


State whether the following statement is True or False:

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


State whether the following statement is True or False:

Corr(x, x) = 0


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


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 ______


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


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.


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`


If byx > 1 then bxy is _______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×